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Unique continuation property for biharmonic hypersurfaces in spheres Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210913
Bibi, Hiba, Loubeau, Eric, Oniciuc, CezarWe prove a unique continuation theorem for nonminimal biharmonic hypersurfaces of spheres, based on Aronszajn’s 1957 article. Under the right hypotheses, this result shows that, for these immersions, CMC on an open subset implies globally CMC. We then deduce new rigidity theorems to support the Conjecture that biharmonic submanifolds of Euclidean spheres must be of constant mean curvature.

On blowup formula of integral Bott–Chern cohomology Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210909
Chen, Youming, Yang, SongRecently, the blowup formulae of cohomologies on complex manifolds have been extensively studied. The purpose of this paper is to give a proof for the blowup formula of integral Bott–Chern cohomology on compact complex manifolds in terms of relative Dolbeault sheaves.

Upper bounds for Steklov eigenvalues of subgraphs of polynomial growth Cayley graphs Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210906
Tschanz, LéonardWe study the Steklov problem on a subgraph with boundary \((\Omega ,B)\) of a polynomial growth Cayley graph \(\Gamma\). For \((\Omega _l, B_l)_{l=1}^\infty\) a sequence of subgraphs of \(\Gamma\) such that \(\Omega _l \longrightarrow \infty\), we prove that for each \(k \in {\mathbb {N}}\), the kth eigenvalue tends to 0 proportionally to \(1/B^{\frac{1}{d1}}\), where d represents the growth rate

The Weyl functional on 4manifolds of positive Yamabe invariant Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210823
Sung, ChanyoungIt is shown that on every closed oriented Riemannian 4manifold (M, g) with positive scalar curvature, $$\begin{aligned} \int _MW^+_g^2d\mu _{g}\ge 2\pi ^2(2\chi (M)+3\tau (M))\frac{8\pi ^2}{\pi _1(M)}, \end{aligned}$$ where \(W^+_g\), \(\chi (M)\) and \(\tau (M)\), respectively, denote the selfdual Weyl tensor of g, the Euler characteristic and the signature of M. This generalizes Gursky’s inequality

On the Markus conjecture in convex case Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210817
Jo, Kyeonghee, Kim, InkangIn this paper, we show that any convex affine domain with a nonempty limit set on the boundary under the action of the identity component of the automorphism group cannot cover a compact affine manifold with a parallel volume, which is a positive answer to the Markus conjecture for convex case. Consequently, we show that the Markus conjecture is true for convex affine manifolds of dimension ≤ 5.

Polar varieties and bipolar surfaces of minimal surfaces in the nsphere Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210806
Moriya, KatsuhiroFor a given minimal surface in the nsphere, two ways to construct a minimal surface in the msphere are given. One way constructs a minimal immersion. The other way constructs a minimal immersion which may have branch points. The branch points occur exactly at each point where the original minimal surface is geodesic. If a minimal surface in the 3sphere is given, then these ways construct Lawson’s

Fundamental gaps of spherical triangles Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210730
Seto, Shoo, Wei, Guofang, Zhu, XuwenWe show that the spherical equilateral triangle of diameter \(\frac{\pi }{2}\) is a strict local minimizer of the fundamental gap on the space of the spherical triangles with diameter \(\frac{\pi }{2}\), which partially extends LuRowlett’s result–(Commun Math Phys 319(1): 111–145, 2013) from the plane to the sphere.

On length measures of planar closed curves and the comparison of convex shapes Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210726
Nicolas Charon, Thomas PierronIn this paper, we revisit the notion of length measures associated to planar closed curves. These are a special case of area measures of hypersurfaces which were introduced early on in the field of convex geometry. The length measure of a curve is a measure on the circle \(\mathbb {S}^1\) that intuitively represents the length of the portion of curve which tangent vector points in a certain direction

The spinor and tensor fields with higher spin on spaces of constant curvature Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210726
Yasushi Homma, Takuma TomihisaIn this article, we give all the Weitzenböcktype formulas among the geometric firstorder differential operators on the spinor fields with spin \(j+1/2\) over Riemannian spin manifolds of constant curvature. Then, we find an explicit factorization formula of the Laplace operator raised to the power \(j+1\) and understand how the spinor fields with spin \(j+1/2\) are related to the spinors with lower

Taut contact hyperbolas on threemanifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210722
Domenico PerroneIn this paper, we introduce the notion of taut contact hyperbola on threemanifolds. It is the hyperbolic analogue of the taut contact circle notion introduced by Geiges and Gonzalo (Invent. Math., 121: 147–209, 1995), (J. Differ. Geom., 46: 236–286, 1997). Then, we characterize and study this notion, exhibiting several examples, and emphasizing differences and analogies between taut contact hyperbolas

Deformations of Dolbeault cohomology classes for Lie algebra with complex structures Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210722
Wei XiaIn this paper, we study deformations of complex structures on Lie algebras and its associated deformations of Dolbeault cohomology classes. A complete deformation of complex structures is constructed in a way similar to the Kuranishi family. The extension isomorphism is shown to be valid in this case. As an application, we prove that given a family of leftinvariant deformations \(\{M_t\}_{t\in B}\)

A volume comparison theorem for characteristic numbers Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210721
Daniel LuckhardtWe show that assuming lower bounds on the Ricci curvature and the injectivity radius the absolute value of certain characteristic numbers of a Riemannian manifold, including all Pontryagin and Chern numbers, is bounded proportionally to the volume. The proof relies on Chern–Weil theory applied to a connection constructed from Euclidean connections on charts in which the metric tensor is harmonic and

Periodic magnetic geodesics on Heisenberg manifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210719
Jonathan Epstein, Ruth Gornet, Maura B. MastWe study the dynamics of magnetic flows on Heisenberg groups, investigating the extent to which properties of the underlying Riemannian geometry are reflected in the magnetic flow. Much of the analysis, including a calculation of the Mañé critical value, is carried out for \((2n+1)\)dimensional Heisenberg groups endowed with any left invariant metric and any exact, leftinvariant magnetic field. In

Conformal scattering theory for the linearized gravity fields on Schwarzschild spacetime Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210713
Truong Xuan PhamWe provide in this paper a first step to obtain the conformal scattering theory for the linearized gravity fields on the Schwarzschild spacetime by using the conformal geometric approach. We will show that the existing decay results for the solutions of the Regge–Wheeler and Zerilli equations obtained recently by Anderson et al. (Ann. Henri Poincaré 21:61–813, 2020) are sufficient to obtain the conformal

Hierarchies of holonomy groupoids for foliated bundles Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210713
Lachlan E. MacDonaldWe give a new construction of the holonomy groupoid of a regular foliation in terms of a partial connection on a diffeological principal bundle of germs of transverse parametrisations, which may be viewed as a systematisation of Winkelnkemper’s original construction using ideas from gauge theory. We extend these ideas to construct a novel holonomy groupoid for any foliated bundle, which we prove sits

Existence, uniqueness and regularity of the projection onto differentiable manifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210701
Gunther Leobacher, Alexander SteinickeWe investigate the maximal open domain \({\mathscr {E}}(M)\) on which the orthogonal projection map p onto a subset \(M\subseteq {{\mathbb {R}}}^d\) can be defined and study essential properties of p. We prove that if M is a \(C^1\) submanifold of \({{\mathbb {R}}}^d\) satisfying a Lipschitz condition on the tangent spaces, then \({\mathscr {E}}(M)\) can be described by a lower semicontinuous function

On the generalized $$\text {SO}(2n,{{\mathbb {C}}})$$ SO ( 2 n , C ) opers Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210630
Indranil Biswas, Laura P. Schaposnik, Mengxue YangSince their introduction by Beilinson–Drinfeld (Opers, 1993. arXiv math/0501398; Quantization of Hitchin’s integrable system and Hecke eigensheaves, 1991), opers have seen several generalizations. In Biswas et al. (SIGMA Symmetry Integr Geom Methods Appl 16:041, 2020), a higher rank analog was studied, named generalized Bopers, where the successive quotients of the oper filtration are allowed to have

The anomaly flow on nilmanifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210628
Mattia Pujia, Luis UgarteWe study the Anomaly flow on 2step nilmanifolds with respect to any Hermitian connection in the Gauduchon line. In the case of flat holomorphic bundle, the general solution to the Anomaly flow is given for any initial invariant Hermitian metric. The solutions depend on two constants \(K_1\) and \(K_2\), and we study the qualitative behaviour of the Anomaly flow in terms of their signs, as well as

Gradient ambient obstruction solitons on homogeneous manifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210625
Erin GriffinWe examine homogeneous solitons of the ambient obstruction flow and, in particular, prove that any compact ambient obstruction soliton with constant scalar curvature is trivial. Focusing on dimension 4, we show that any homogeneous gradient Bach soliton that is steady must be Bach flat, and that the only nonBachflat shrinking gradient solitons are product metrics on \(\mathbb {R}^2\times S^2\) and

On the fluid ball conjecture Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210621
Fernando Coutinho, Benedito Leandro, Hiuri F. S. ReisThe fluid ball conjecture states that a static perfect fluid spacetime is spherically symmetric. In this paper we construct a Robinson’s divergence formula for the static perfect fluid spacetime. Inspired by this conjecture, a rigidity result for the spatial factor of a static perfect fluid spacetime satisfying some boundary conditions is proved, provided that an equation of state holds.

Symmetric solutions of the singular minimal surface equation Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210621
Ulrich Dierkes, Nico GrohWe classify all rotational symmetric solutions of the singular minimal surface equation in both cases \(\alpha <0\) and \(\alpha >0\). In addition, we discuss further geometric and analytic properties of the solutions, in particular stability, minimizing properties and Bernsteintype results.

Positive Hermitian curvature flow on nilpotent and almostabelian complex Lie groups Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210609
James StanfieldWe study the positive Hermitian curvature flow on the space of leftinvariant metrics on complex Lie groups. We show that in the nilpotent case, the flow exists for all positive times and subconverges in the Cheeger–Gromov sense to a soliton. We also show convergence to a soliton when the complex Lie group is almost abelian. That is, when its Lie algebra admits a (complex) codimension one abelian

Harmonic mappings between singular metric spaces Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210531
ChangYu GuoIn this paper, we survey the existence, uniqueness and interior regularity of solutions to the Dirichlet problem associated with various energy functionals in the setting of mappings between singular metric spaces. Based on known ideas and techniques, we separate the necessary analytical assumptions to axiomatizing the theory in the singular setting. More precisely, (1) we extend the existence result

Banach manifold structure and infinitedimensional analysis for causal fermion systems Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210531
Felix Finster, Magdalena LottnerA mathematical framework is developed for the analysis of causal fermion systems in the infinitedimensional setting. It is shown that the regular spacetime point operators form a Banach manifold endowed with a canonical Fréchetsmooth Riemannian metric. The socalled expedient differential calculus is introduced with the purpose of treating derivatives of functions on Banach spaces which are differentiable

Relative nonpluripolar product of currents Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210526
DucViet VuLet X be a compact Kähler manifold. Let \(T_1, \ldots , T_m\) be closed positive currents of bidegree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the nonpluripolar product relative to T of \(T_1, \ldots , T_m\). We recover the wellknown nonpluripolar product of \(T_1, \ldots , T_m\) when T is the current of integration along X. Our main results are a monotonicity property

The $$L^p$$ L p Calderón–Zygmund inequality on noncompact manifolds of positive curvature Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210521
Ludovico Marini, Giona VeronelliWe construct, for \(p>n\), a concrete example of a complete noncompact ndimensional Riemannian manifold of positive sectional curvature which does not support any \(L^p\)Calderón–Zygmund inequality: $$\begin{aligned}\Vert {{\,\mathrm{Hess}\,}}\varphi \Vert _{L^p}\le C(\Vert \varphi \Vert _{L^p}+\Vert \Delta \varphi \Vert _{L^p}), \qquad \forall \,\varphi \in C^{\infty }_c(M). \end{aligned}$$ The

Isothermic constrained Willmore tori in 3space Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210520
Lynn Heller, Sebastian Heller, Cheikh Birahim NdiayeWe show that the homogeneous and the 2lobe Delaunay tori in the 3sphere provide the only isothermic constrained Willmore tori in 3space with Willmore energy below \(8\pi \). In particular, every constrained Willmore torus with Willmore energy below \(8\pi \) and nonrectangular conformal class is nondegenerated.

Enlargeable lengthstructure and scalar curvatures Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210519
Jialong DengWe define enlargeable lengthstructures on closed topological manifolds and then show that the connected sum of a closed nmanifold with an enlargeable Riemannian lengthstructure with an arbitrary closed smooth manifold carries no Riemannian metrics with positive scalar curvature. We show that closed smooth manifolds with a locally CAT(0)metric which is strongly equivalent to a Riemannian metric

Weak curvatures of irregular curves in highdimensional Euclidean spaces Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210518
Domenico Mucci, Alberto SaraccoWe deal with a robust notion of weak normals for a wide class of irregular curves defined in Euclidean spaces of high dimension. Concerning polygonal curves, the discrete normals are built up through a Gram–Schmidt procedure applied to consecutive oriented segments, and they naturally live in the projective space associated with the Gauss hypersphere. By using sequences of inscribed polygonals with

On the nonexistence of common submanifolds of Kähler manifolds and complex space forms Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210510
Xiaoliang Cheng, Yihong HaoTwo Kähler manifolds are called relatives if they admit a common Kähler submanifold with their induced metrics. In this paper, we provide a sufficient condition to determine whether a real analytic Kähler manifold is not a relative to a complex space form equipped with its canonical metric. As an application, we show that minimal domains, bounded homogeneous domains and some Hartogs domains equipped

Selfintersections of closed parametrized minimal surfaces in generic Riemannian manifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210427
John Douglas MooreThis article shows that for generic choice of Riemannian metric on a compact oriented manifold M of dimension four, the tangent planes at any selfintersection \(p \in M\) of any prime closed parametrized minimal surface in M are not simultaneously complex for any orthogonal complex structure on M at p. This implies via geometric measure theory that \(H_2(M;{{\mathbb {Z}}})\) is generated by homology

The contact mappings of a flat (2,3,5)distribution Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210426
Alex D. AustinLet Ω and Ω′ be open subsets of a flat (2,3,5)distribution. We show that a C1smooth contact mapping f: Ω → Ω′ is a \(C^\infty\)smooth contact mapping. Ultimately, this is a consequence of the rigidity of the associated stratified Lie group. (The Tanaka prolongation of the Lie algebra is of finite type.) The conclusion is reached through a careful study of some differential identities satisfied by

Homogeneous nondegenerate 3(α,δ)Sasaki manifolds and submersions over quaternionic Kähler spaces Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210426
Ilka Agricola, Giulia Dileo, Leander SteckerWe show that every 3\((\alpha ,\delta )\)Sasaki manifold of dimension \(4n + 3\) admits a locally defined Riemannian submersion over a quaternionic Kähler manifold of scalar curvature \(16n(n+2)\alpha \delta\). In the nondegenerate case we describe all homogeneous 3\((\alpha ,\delta )\)Sasaki manifolds fibering over symmetric Wolf spaces and over their noncompact dual symmetric spaces. If \(\alpha

Existence of a complete holomorphic vector field via the Kähler–Einstein metric Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210426
YoungJun Choi, KangHyurk LeeIn this paper, we study the existence of a complete holomorphic vector field on a strongly pseudoconvex complex manifold admitting a negatively curved complete Kähler–Einstein metric and a discrete sequence of automorphisms. Using the method of potential scaling, we will show that there is a potential function of the Kähler–Einstein metric whose differential has a constant length. Then, we will construct

The classification of flat Riemannian metrics on the plane Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210419
Vincent E. Coll, Lee B. WhittWe classify all smooth flat Riemannian metrics on the twodimensional plane. In the complete case, it is well known that these metrics are isometric to the Euclidean metric. In the incomplete case, there is an abundance of naturally occurring, nonisometric metrics that are relevant and useful. Remarkably, the study and classification of all flat Riemannian metrics on the plane—as a subject—is new

Typical field lines of Beltrami flows and boundary field line behaviour of Beltrami flows on simply connected, compact, smooth manifolds with boundary Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210412
Wadim GernerWe characterise the boundary field line behaviour of Beltrami flows on compact, connected manifolds with vanishing first de Rham cohomology group. Namely we show that except for an at most nowhere dense subset of the boundary, on which the Beltrami field may vanish, all other field lines at the boundary are smoothly embedded 1manifolds diffeomorphic to \({\mathbb {R}}\), which approach the zero set

Holomorphic maps into Grassmann manifolds (harmonic maps into Grassmann manifolds III) Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210322
Yasuyuki NagatomoA wellknown Calabi’s rigidity theorem on holomorphic isometric immersions into the complex projective space is generalized to the case that the target is the complex Grassmann manifolds. Our strategy is to use the differential geometry of vector bundles and a generalization of do Carmo and Wallach theory developed in Nagatomo (Harmonic maps into Grassmann manifolds. arXiv:mathDG/1408.1504). We introduce

Sharp upper diameter bounds for compact shrinking Ricci solitons Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210315
JiaYong WuWe give a sharp upper diameter bound for a compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman’s entropy functional. The sharp cases could occur at round spheres. The proof mainly relies on a sharp logarithmic Sobolev inequality of gradient shrinking Ricci solitons and a Vitalitype covering argument.

The gluing formula, conformal scaling, and geometry Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210315
Klaus Kirsten, Yoonweon LeeWe exploit conformal transformations of gluing formulas to realize connections between zeta functions of Laplacians and associated DirichlettoNeumann map zeta functions. Furthermore, the geometric content in gluing formulas is identified and explicit results are given for a threedimensional manifold.

Upper bounds for the ground state energy of the Laplacian with zero magnetic field on planar domains Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210315
Bruno Colbois, Alessandro SavoWe obtain upper bounds for the first eigenvalue of the magnetic Laplacian associated to a closed potential 1form (hence, with zero magnetic field) acting on complex functions of a planar domain \(\Omega \), with magnetic Neumann boundary conditions. It is well known that the first eigenvalue is positive whenever the potential admits at least one nonintegral flux. By gauge invariance, the lowest eigenvalue

Correction to: Killing spinorvalued forms and their integrability conditions Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210310
Petr Somberg, Petr ZimaThe authors gratefully acknowledge the support of the Grants GA1906357S, GAUK 700217 and SVV2017260456.

Skew Killing spinors in four dimensions Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210305
Nicolas Ginoux, Georges Habib, Ines KathThis paper is devoted to the classification of 4dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor \(\psi \) is a spinor that satisfies the equation \(\nabla _X\psi =AX\cdot \psi \) with a skewsymmetric endomorphism A. We consider the degenerate case, where the rank of A is at most two everywhere and the nondegenerate case, where the rank of A is four everywhere

Locally conformally flat Kähler and paraKähler manifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210304
M. FerreiroSubrido, E. GarcíaRío, R. VázquezLorenzoWe complete the classification of locally conformally flat Kähler and paraKähler manifolds, describing all possible nonflat curvature models for Kähler and paraKähler surfaces.

Schauder estimates on smooth and singular spaces Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210304
Yaoting Gui, Hao YinIn this paper, we present a proof of Schauder estimate on Euclidean space and use it to generalize Donaldson’s Schauder estimate on space with conical singularities in the following two directions. The first is that we allow the total cone angle to be larger than 2\(\pi \) and the second is that we discuss higherorder estimates.

Quaternionic contact 4 n + 3manifolds and their 4 n quotients Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210303
Yoshinobu KamishimaWe study some types of qcEinstein manifolds with zero qcscalar curvature introduced by S. Ivanov and D. Vassilev. Secondly, we shall construct a family of quaternionic Hermitian metrics \((g_a,\{J_\alpha \}_{\alpha =1}^3)\) on the domain Y of the standard quaternion space \({\mathbb {H}}^n\) one of which, say \((g_a,J_1)\) is a Bochner flat Kähler metric. To do so, we deform conformally the standard

Isoperimetric estimates in lowdimensional Riemannian products Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210302
Juan Miguel Ruiz, Areli Vázquez JuárezLet \((T^k,h_k)=(S_{r_1}^1\times S_{r_2}^1 \times \cdots \times S_{r_k}^1, dt_1^2+dt_2^2+\cdots +dt_k^2)\) be flat tori, \(r_k\ge \cdots \ge r_2\ge r_1>0\) and \(({\mathbb {R}}^n,g_E)\) the Euclidean space with the flat metric. We compute the isoperimetric profile of \((T^2\times {\mathbb {R}}^n, h_2+g_E)\), \(2\le n\le 5\), for small and big values of the volume. These computations give explicit lower

Resolution of fourdimensional symplectic orbifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210217
Lucía MartínMerchán, Juan RojoWe give a method to resolve fourdimensional symplectic orbifolds making use of techniques from complex geometry and gluing of symplectic forms. We provide some examples to which the resolution method applies.

Completeness in affine and statistical geometry Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210210
Barbara OpozdaWe begin the study of completeness of affine connections, especially those on statistical manifolds or on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.

A shape optimization problem for the first mixed Steklov–Dirichlet eigenvalue Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210201
DongHwi SeoWe consider a shape optimization problem for the first mixed Steklov–Dirichlet eigenvalues of domains bounded by two balls in twopoint homogeneous space. We give a geometric proof which is motivated by Newton’s shell theorem.

Embeddedness, convexity, and rigidity of hypersurfaces in product spaces Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210129
Ronaldo Freire de LimaWe establish the following Hadamard–Stokertype theorem: Let \(f:M^n\rightarrow \mathscr{H} ^{\,\,\, n}\times \mathbb{R}\) be a complete connected hypersurface with positive definite second fundamental form, where \(\mathscr{H} ^{\,\,\, n}\) is a Hadamard manifold. If the height function of f has a critical point, then it is an embedding and M is homeomorphic to \(\mathbb{S}^n\) or \(\mathbb{R}^n.\)

Twostep homogeneous geodesics in pseudoRiemannian manifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210118
Andreas Arvanitoyeorgos, Giovanni Calvaruso, Nikolaos Panagiotis SourisGiven a homogeneous pseudoRiemannian space \((G/H,\langle \ , \ \rangle),\) a geodesic \(\gamma :I\rightarrow G/H\) is said to be twostep homogeneous if it admits a parametrization \(t=\phi (s)\) (s affine parameter) and vectors X, Y in the Lie algebra \({\mathfrak{g}}\), such that \(\gamma (t)=\exp (tX)\exp (tY)\cdot o\), for all \(t\in \phi (I)\). As such, twostep homogeneous geodesics are a natural

On the boundary injectivity radius of Buser–Colbois–DodziukMargulis tubes Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210106
Luca F. Di CerboWe give a lower bound on the boundary injectivity radius of the Margulis tubes with smooth boundary constructed by Buser, Colbois, and Dodziuk. This estimate depends on the dimension and a curvature bound only.

Conformally Kähler, Einstein–Maxwell metrics on Hirzebruch surfaces Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20210106
Isaque Viza de SouzaIn this note, we prove that a special family of Killing potentials on certain Hirzebruch complex surfaces, found by Futaki and Ono [ 18 ], gives rise to new conformally Kähler, Einstein–Maxwell metrics. The correspondent Kähler metrics are ambitoric [ 7 , 9 ] but they are not given by the Calabi ansatz [ 31 ]. This answers in positive questions raised in [ 18 , 19 ].

Global properties of toric nearly Kähler manifolds Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20201221
Kael DixonWe study toric nearly Kahler manifolds, extending the work of Moroianu and Nagy. We give a description of the global geometry using multimoment maps. We then investigate polynomial and radial solutions to the toric nearly Kahler equation.

On certain classes of $$\mathbf{Sp}(4,\mathbb{R})$$ Sp ( 4 , R ) symmetric $$G_2$$ G 2 structures Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20201119
Paweł NurowskiWe find two different families of \(\mathbf{Sp}(4,\mathbb{R})\) symmetric \(G_2\) structures in seven dimensions. These are \(G_2\) structures with \(G_2\) being the split real form of the simple exceptional complex Lie group \(G_2\). The first family has \(\tau _2\equiv 0\), while the second family has \(\tau _1\equiv \tau _2\equiv 0\), where \(\tau _1\), \(\tau _2\) are the celebrated \(G_2\)invariant

Infinitesimal homogeneity and bundles Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20201109
Arash Bazdar, Andrei Teleman 
The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their blowups Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20201106
Michael AlbaneseShortly after the introduction of SeibergWitten theory, LeBrun showed that the sign of the Yamabe invariant of a compact Kahler surface is determined by its Kodaira dimension. In this paper, we show that LeBrun's Theorem is no longer true for nonKahler surfaces. In particular, we show that the Yamabe invariants of Inoue surfaces and their blowups are all zero. We also take this opportunity to record

Orthogonal biinvariant complex structures on metric Lie algebras Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20201104
Jonas DeréThis paper studies how many orthogonal biinvariant complex structures exist on a metric Lie algebra over the real numbers. Recently, it was shown that irreducible Lie algebras which are additionally $2$step nilpotent admit at most one orthogonal biinvariant complex structure up to sign. The main result generalizes this statement to metric Lie algebras with any number of irreducible factors and which

Jacobi relations on naturally reductive spaces Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20201029
Tillmann Jentsch, Gregor WeingartNaturally reductive spaces, in general, can be seen as an adequate generalization of Riemannian symmetric spaces. Nevertheless, there are some that are closer to symmetric spaces than others. On the one hand, there is the series of Hopf fibrations over complex space forms, including the Heisenberg groups with their metrics of type H. On the other hand, there exist certain naturally reductive spaces

Reflection principle for lightlike line segments on maximal surfaces Ann. Glob. Anal. Geom. (IF 0.846) Pub Date : 20201023
Shintaro Akamine, Hiroki FujinoAs in the case of minimal surfaces in the Euclidean 3space, the reflection principle for maximal surfaces in the LorentzMinkowski 3space asserts that if a maximal surface has a spacelike line segment L , the surface is invariant under the $$180^\circ$$ 180 ∘ rotation with respect to L . However, such a reflection property does not hold for lightlike line segments on the boundaries of maximal surfaces