In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms of 2-forms on 0-jet space. We use this observation to find a new class of multivalued solutions for an arbitrary thermodynamic state model and discuss singularities of their projections to the space of independent variables

We introduce a covariant formulation of Barbero–Immirzi connections, which are used in Loop Quantum Gravity to describe gravity. We show that Barbero–Immirzi connections can be uniquely defined out of a given spin connection for any (n+1)-dimensional lorentzian manifold which is spin. A remarkable result is that the presence of a real Barbero–Immirzi parameter is a feature unique to the 4-dimensional

In this article, a new (2+1)-dimensional extension of the Hietarinta equation is proposed. Two classes of lump and line rogue wave solutions are obtained for this equation by means of the Hirota bilinear method. These solutions, which are algebraically decaying rational solutions, arise from quadratic function solutions to the associated bilinear equation through a logarithmic transformation. Necessary

A brief review of the essentials behind the construction of a Chern-Simons-like brane action from the Large N limit of Exceptional Jordan Matrix Models paves the way to the construction of actions for membranes and p-branes moving in octonionic-spacetime backgrounds endowed with octonionic-valued metrics. It is found that the action of a membrane moving in spacetime backgrounds endowed with an octonionic-valued

In this paper, we study a (2+1)-dimensional Boussinesq type equation. By applying the Hirota direct method, lump and line rogue wave solutions are presented with the aid of symbolic computations. The solutions are expressed in terms of a set of restricted parameters with necessary and sufficient conditions that guarantee their existence. An interesting result is that when the parameters meet the rank

In this article we have showed that a gradient ρ-Einstein soliton with a vector field of bounded norm and satisfying some other conditions is isometric to the Euclidean sphere. Later, we have proved that a non-trivial complete gradient ρ-Einstein soliton with finite weighted Dirichlet integral and certain restriction on Ricci curvature must be of constant scalar curvature and steady Ricci flat. Finally

In this paper we study the so-called sigma form of the second Painlevé hierarchy. To obtain this form, we use some properties of the Hamiltonian structure of the second Painlevé hierarchy and of the Lenard operator.

This paper is devoted to the advance in the project of systematic description of colored knot polynomials started in [1] – explicit calculation of the inclusive Racah matrices for representation R=[3,3]. This is made possible by a powerful technique which we suggest in this paper – the use of highest weight method in the basis of Gelfand-Tseitlin tables. Our result allows one to evaluate and investigate

By analyzing the Ricci star tensor Ric*, we study the harmonic almost complex structure in maximal flag manifolds. We show that flag manifolds have diagonal Ric* tensor. Using the concept of ⁎Einstein manifolds, we study the stability of the invariant almost complex structure and show examples of stables parabolic almost complex structures on maximal flag manifolds.

Our aim is to characterize the Lorentzian manifolds endowed with a type of semi-symmetric non-metric connection. It is proven that a Lorentzian manifold with a type of semi-symmetric non-metric connection is a GRW space-time. To minimize the gap between the RW space-time and the GRW space-time, we establish a bridge between them. It is shown that a weakly Ricci symmetric GRW space-time is a stiff matter

We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop quite a general framework of noncommutative complex geometry that subsumes the one in [12]. We present transverse complex and Kähler structures as examples and discuss several other examples. Relation with past literature is described.

In a previous paper, the first two named authors established an isomorphism between the moduli space of framed flags of sheaves on the projective plane and the moduli space of stable representations of a certain quiver. In the present note, we substitute one of the claims made, namely [5, Theorem 17], for a weaker claim regarding the existence of unobstructed points in the quiver moduli space. We also

Let (g,X) be a Sasaki-Ricci soliton on a Sasakian manifold S. We prove that if (S,g) admits a local Sasakian immersion in a Sasakian space form S(N,c) of constant ϕ-sectional curvature c, then S is η-Einstein and its η-Einstein constants are a linear function of c with rational coefficients. Moreover, if c≤−3, S is locally equivalent to the Sasakian space form S(n,c). Further results are obtained in

We obtain sharp inequalities involving the Ricci curvature and the scalar curvature for anti-invariant Riemannian submersions from Sasakian space forms onto Riemannian manifolds.

The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal vector field or a concurrent vector field. Finally, we study Ricci soliton on some

In the present paper, we introduce a class of infinite Lie conformal superalgebras S(p), which are closely related to Lie conformal algebras of extended Block type defined in [6]. Then all finite non-trivial irreducible conformal modules over S(p) for p∈C⁎ are completely classified. As an application, we also present the classifications of finite non-trivial irreducible conformal modules over finite

In this paper, firstly we obtain the Gauss map (unit normal vector field) of a 2-ruled hypersurface in Euclidean 4-space with the aid of its general parametric equation. After, we obtain Gaussian and mean curvatures of the 2-ruled hypersurface and give some characterizations about its minimality. Finally, we deal with the first and second Laplace–Beltrami operators of 2-ruled hypersurfaces in E4 and

We study the properties of Ricci curvature of g-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the transverse manifold of the characteristic foliation are investigated. In particular, sufficient conditions are found under which the g-manifold can be a Ricci soliton or a gradient

We consider evolution equations for curves in the 3-dimensional sphere S3 that are invariant under the group SU(2,1) of pseudoconformal transformations, which preserves the standard contact structure on the sphere. In particular, we investigate how invariant evolutions of Legendrian and transverse curves induce both new and well-known integrable systems and hierarchies at the level of their geometric

Given a compact complex manifold X and a integrable Beltrami differential ϕ∈A0,1(X,TX1,0), we introduce a double complex structure on A•,•(X) naturally determined by ϕ and study its Bott-Chern cohomology. In particular, we establish a deformation theory for Bott-Chern cohomology and use it to compute the deformed Bott-Chern cohomology for the Iwasawa manifold and the holomorphically parallelizable

We use two non-Riemannian curvature tensors, the χ-curvature and the mean Berwald curvature to characterise a class of Finsler metrics admitting first integrals. This class includes Finsler metrics of constant flag curvature.

In this paper, we derive a Weierstrass-type representation formula for regular lightlike surfaces in Lorentz-Minkowski 3-space. It allows a local parametrization of a regular lightlike surface by a pair of holomorphic and meromorphic dual functions. We also discuss definition of minimal lightlike surfaces in Lorentz-Minkowski 3-space in this context by relating it to the class of surfaces that are

We study global transverse Poincaré sections and give topological obstructions to their existence. We prove that any energy hypersurface equipped with a global transverse Poincaré section has an induced cosymplectic structure. We give a family of Hamiltonian systems with global Poincaré sections of all possible topologies. Finally, we address the question of when a compact hypersurface of a symplectic

We find the necessary and sufficient conditions for a sequential warped product manifold to be a quasi-Einstein manifold. We also investigate the necessary conditions for a sequential standard static space-time and a sequential generalized Robertson-Walker space-time to be a manifold of quasi-constant curvature.

We consider a family of α-connections defined by a pair of generalized dual quasi-statistical connections (∇ˆ,∇ˆ∗) on the generalized tangent bundle (TM⊕T∗M,hˇ) and determine their curvature, Ricci curvature and scalar curvature. Moreover, we provide the necessary and sufficient condition for ∇ˆ∗ to be an equiaffine connection and we prove that if h is symmetric and ∇h=0, then (TM⊕T∗M,hˇ,∇ˆ(α),∇ˆ(−α))

Given a compact Kähler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of stable bundles as an open subspace. For local models invariant generalized Weil-Petersson forms exist on the parameter spaces, which are restrictions of symplectic forms

Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces (M=G∕H,g) whose geodesics are orbits of one-parameter subgroups of G. The corresponding metric g is called a geodesic orbit metric. We study the geodesic orbit spaces of the form (Sp(n)∕Sp(n1)×⋯×Sp(ns),g), with 0

We compare the description of the M-theory form fields via cohomotopy versus that via integral cohomology. The conditions for lifting the latter to the former are identified using obstruction theory in the form of Postnikov towers, where torsion plays a central role. A subset of these conditions are shown to correspond compatibly to existing consistency conditions, while the rest are new and point

We present some new constructions of Lie algebroids starting from vector fields on manifold M. The tangent bundle TM possess a natural structure of Lie algebroid, but we use these fields to construct a collection of interesting new algebroid structures. Next, we show that these constructions can be used in a more general situation, starting from an arbitrary Lie algebroid over M. In the final step

We consider a linear combination of the potential KP equation and the BKP equation, and call it a combined pKP–BKP equation. We prove that the combined pKP–BKP equation satisfies the Hirota N-soliton condition and thus it possesses an N-soliton solution. The proof is an application of an algorithm to compare degrees of homogeneous polynomials associated with the Hirota function in N wave vectors.

Based on Darboux transformations for the supersymmetric constrained KP(ScKP) hierarchy, we construct the supersymmetric constrained B type KP(ScBKP) and supersymmetric constrained C type KP(ScCKP) hierarchies of Manin–Radul and Jacobian types, and derive Darboux transformations on them. On the basis of the seed solutions, the new solutions can be generated by these Darboux transformations.

The purpose of this paper is to show the relationship in all dimensions between the structural (diffraction pattern) aspect of tilings (described by Čech cohomology of the tiling space) and the spectral properties (of Hamiltonians defined on such tilings) defined by K-theory, and to show their equivalence in dimensions ≤ 3. A theorem makes precise the conditions for this relationship to hold. It can

Nonlinear oscillators described by polynomial Liénard differential equations arise in a variety of mathematical and physical applications. For a family of generalized Duffing–van der Pol oscillators we classify Darboux integrable cases and explicitly construct the corresponding generalized Darboux first integrals. We demonstrate that Darboux integrability is in strong correlation with the linearizability

The article is a continuation of Hu and Zhuang (2021), we construct another admissible quantum affine algebra Uq(sl̂2) of affine type A1(1) with different defining structural constants and variant q-Serre relations, its present formulae of the quantum root vectors are more involved than those in Hu and Zhuang (2021). We prove that as Hopf algebras, Uq(sl̂2) is neither isomorphic to the standard quantum

We establish the analogue of the Cayley–Hamilton theorem for the quantum matrix algebras of the symplectic type. We construct the algebra in which the quantum characteristic polynomial acquires a factorized form. The low-dimensional examples and the classical limit are discussed.

We consider a d-dimensional well-formed weighted projective space P(w¯) as a toric variety associated with a fan Σ(w¯) in Nw¯⊗R whose 1-dimensional cones are spanned by primitive vectors v0,v1,…,vd∈Nw¯ generating a lattice Nw¯ and satisfying the linear relation ∑iwivi=0. For any fixed dimension d, there exist only finitely many weight vectors w¯=(w0,…,wd) such that P(w¯) contains a quasi-smooth Calabi–Yau

This work is divided in two cases. In the first case, we consider a spin manifold M as the set of fixed points of an S1-action on a spin manifold X, and in the second case we consider the spin manifold M as the set of fixed points of an S1-action on the loop space of M. For each case, we build on M a vector bundle, a connection and a set of bundle endomorphisms. These objects are used to build global

In this second in a series paper we complete our classification of hypercomplex manifolds, on which a compact group of automorphisms acts transitively. The description of the spaces as well as the proofs of our results use only the structure theory of reductive groups.

First we introduce the notion of Ricci semi-symmetric real hypersurfaces in the complex quadric Qm=SOm+2∕SOmSO2 and show that the unit normal vector field N is singular. Next we give a new classification of real hypersurfaces in the complex quadric Qm=SOm+2∕SOmSO2 with semi-symmetric Ricci tensor.

We provide necessary and sufficient conditions for some particular couples (g,∇) of pseudo-Riemannian metrics and affine connections to be statistical structures if we have gradient almost Einstein, almost Ricci, almost Yamabe solitons, or a more general type of solitons on the manifold. In particular cases, we establish a formula for the volume of the manifold and give a lower and an upper bound for

We construct explicit proper p-harmonic functions on rank-one Lie groups of Iwasawa type. This class of Lie groups includes many classical Riemannian manifolds such as the rank-one symmetric spaces of non-compact type, Damek–Ricci spaces, rank-one Einstein solvmanifolds and Carnot spaces.

Let us consider an n-dimensional complex torus TJ=T2n≔ℂn∕2π(Zn⊕TZn). Here, T is a complex matrix of order n whose imaginary part is positive definite. In particular, when we consider the case n=1, the complexified symplectic form of a mirror partner of TJ=T2 is defined by using −1T or T. However, if we assume n≥2 and that T is a singular matrix, we cannot define a mirror partner of TJ=T2n as a natural

Developable surfaces are the special ruled surfaces where the Gaussian curvature of each point vanishes. Tangent developable is the most interesting surface among three fundamental types of developable surfaces. This paper investigates lightlike tangent developable generated by a lightlike base curve in de Sitter 3-space. We first give the topological classification of the lightlike curves which lie

The question of which manifolds are spin or spinc has a simple and complete answer. In this paper we address the same question for spinh manifolds, which are less studied but have appeared in geometry and physics in recent decades. We determine that the first obstruction to being spinh is the fifth integral Stiefel–Whitney class W5. Moreover, we show that every orientable manifold of dimension 7 and

We classify biharmonic and harmonic homomorphisms f:(G,g1)⟶(G,g2) where G is a connected and simply connected three-dimensional unimodular Lie group and g1 and g2 are left invariant Riemannian metrics.

Part I of this paper presented a systematic derivation of the Stokes Dirac structure underlying the port-Hamiltonian model of ideal fluid flow on Riemannian manifolds. Starting from the group of diffeomorphisms as a configuration space for the fluid, the Stokes Dirac structure is derived by Poisson reduction and then augmented by boundary ports and distributed ports. The additional boundary ports have

In this two-parts paper, we present a systematic procedure to extend the known Hamiltonian model of ideal inviscid fluid flow on Riemannian manifolds in terms of Lie-Poisson structures to a port-Hamiltonian model in terms of Stokes-Dirac structures. The first novelty of the presented model is the inclusion of non-zero energy exchange through, and within, the spatial boundaries of the domain containing

Let C be a chain-like curve having n smooth components and n−1 nodes, where n≥2. Let E be a vector bundle on C and V⊆H0(E) be a linear subspace generating E. We investigate the (semi)stability of the kernel bundle ME,V associated to (E,V).

In this paper, we studied the boost operator in the setting of su(1|1)2. We find a family of different algebras where such an operator can consistently appear, which we classify according to how the two copies of the su(1|1) interact with each other. Finally, we construct coproduct maps for each of these algebras and discuss the algebraic relationships among them.

The standard Lie bialgebra structure on an affine Kac–Moody algebra induces a Lie bialgebra structure on the underlying loop algebra and its parabolic subalgebras. In this paper we classify all classical twists of the induced Lie bialgebra structures in terms of Belavin–Drinfeld quadruples up to a natural notion of equivalence. To obtain this classification we first show that the induced bialgebra

We give detailed description for continuous version of the classical IRF-Vertex relation, where on the IRF side we deal with the Calogero–Moser–Sutherland models. Our study is based on constructing modifications of the Higgs bundles of infinite rank over elliptic curve and its degenerations. In this way the previously predicted gauge equivalence between L-A pairs of the Landau–Lifshitz type equations

Under investigation in this paper is the (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation. Based on bilinear method, the multiple rogue wave solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions in the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue waves are obtained

In this paper we prove a local curvature estimate for the κ-LYZ flow over Kähler manifolds introduced in Fei et al. (2019) and Li et al. (2020). In particular, we generalize the long time existence of the flow.

Let M be a connected, simply connected, oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put M×≔M∖{point}. In this paper we prove that if X× is a smooth four-manifold homeomorphic but not necessarily diffeomorphic to M× (more precisely, it carries a smooth structure à la Gompf) then X× can be equipped with a complete Ricci-flat Riemannian metric

We study virtual invariants of Quot schemes parametrizing quotients of dimension at most 1 of the trivial sheaf of rank N on nonsingular projective surfaces. We conjecture that the generating series of virtual K-theoretic invariants are given by rational functions. We prove rationality for several geometries including punctual quotients for all surfaces and dimension 1 quotients for surfaces X with

In this paper, we extend the T-duality isomorphism in Cavalcanti and Gualtieri (2010) from invariant Courant algebroids, to exotic Courant algebroids such that the momentum and winding numbers are exchanged, filling in a gap in the literature.

We consider a family of fermionic star products generalising the fermionic Moyal product. The parameter space contains polarisations used to define quantum Hilbert spaces in geometric quantisation. For each polarisation, we find a star product of fermionic functions on quantum states and show that the star product of any function on a quantum state remains a quantum state. We establish the associativity

We introduce and study the index morphism for leafwise G-transversally elliptic operators on smooth closed foliated manifolds. We prove the usual axioms of excision, multiplicativity and induction for closed subgroups. In the case of free actions, we relate our index class with the Connes-Skandalis index class of the corresponding leafwise elliptic operator on the quotient foliation. Finally we prove

In this paper, first we introduce the notion of a twilled 3-Lie algebra, and construct an L∞-algebra, whose Maurer–Cartan elements give rise to new twilled 3-Lie algebras by twisting. In particular, we recover the Lie 3-algebra whose Maurer–Cartan elements are O-operators (also called relative Rota–Baxter operators) on 3-Lie algebras. Then we introduce the notion of generalized matched pairs of 3-Lie