In this paper, we study a refinement of the Szegö-Radon transform in the hypermonogenic setting. Hypermonogenic functions form a subclass of monogenic functions arising in the study of a modified Dirac operator, which allows for weaker symmetries and also has a strong connection to the hyperbolic metric. In particular, we construct a projection operator from a module of hypermonogenic functions in

A theorem is derived which determines higher order first integrals of autonomous holonomic dynamical systems in a general space, provided the collineations and the Killing tensors –up to the order of the first integral– of the kinetic metric, defined by the kinetic energy of the system, can be computed. The theorem is applied in the case of Newtonian autonomous conservative dynamical systems of two

The asymptotics of characters χkλ(exp⁡(h/k)) of irreducible representations of a compact Lie group G for large values of the scaling factor k are given by Duistermaat-Heckman (DH) integrals over coadjoint orbits of G. This phenomenon generalises to coadjoint orbits of central extensions of loop groups LGˆ and of diffeomorphisms of the circle Diffˆ(S1). We show that the asymptotics of characters of

A class of semilinear heat flows with general nonlinear reaction terms is considered on complete Riemannian manifolds with Ricci curvature bounded from below. Two types of (space-time and space only) gradient estimates are established for positive solutions to the flow, and the corresponding Harnack inequalities are obtained to allow for comparison of solutions. Some specific examples of the reaction

A generalized Bach tensor Bijt with parameter t∈R is introduced. A Riemannian manifold (Mn,g) is called Bt-flat if its generalised Bach tensor Bijt≡0 for some parameter t. In this paper, we first study the rigidity of closed Bt-flat Riemannian manifolds with positive constant scalar curvature. When the dimension n=4, we prove that all Bt-flat manifolds that satisfy a point-wise inequality must be of

We classify, up to equivalences, all abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras. Any grading on a null-filiform Leibniz algebra is toral but there are non-toral gradings on one-parametric filiform Leibniz algebras.

We recall a definition of an asymptotic invariant of classical link, which is called M-invariant. M-invariant is a special Massey integral, this integral has an ergodic form and is generalized for magnetic fields with open magnetic lines in a bounded 3D-domain. We present a proof that this integral is well defined. A combinatorial formula for M-invariant using the Conway polynomial is presented. The

Suppose given a holomorphic and Hamiltonian action of a compact torus T on a polarized Hodge manifold M. Assume that the action lifts to the quantizing line bundle, so that there is an induced unitary representation of T on the associated Hardy space. If in addition the moment map is nowhere zero, for each weight ν the ν-th isotypical component in the Hardy space of the polarization is finite-dimensional

In the contact-geometric formulation of classical thermodynamics distinction is made between the energy and entropy representation. This distinction can be resolved by taking homogeneous coordinates for the intensive variables. It results in a geometric formulation on the cotangent bundle of the manifold of extensive variables, where all geometric objects are homogeneous in the cotangent variables

In this paper we prove that the etale sheafification of the functor arising from the quotient of an algebraic supergroup by a closed subsupergroup is representable by a smooth superscheme.

The multiple Exp-function method is employed for searching the multiple soliton solutions for the (2+1)-dimensional generalized Hirota-Satsuma-Ito (HSI) equation, which contain one-soliton, two-soliton, and triple-soliton kind solutions. Then the lump and interaction solutions are also obtained by the Hirota method for the aforementioned equation. For these obtained solutions, they are mentioned in

In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, (m,ρ)-quasi Einstein manifolds, and gradient Ricci solitons. Then, we obtain some necessary and sufficient conditions about the existence of certain vector fields on the standard static spacetime

We devise a generalisation of the energy momentum-method for studying the stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A generalisation of the relative equilibrium point notion to a non-autonomous realm is provided and studied. Relative equilibrium points of a class of non-autonomous Hamiltonian systems are described via foliated Lie systems, which opens

Rossby-Haurwitz waves on the sphere S2 form a set of exact time-dependent solutions to the Euler equations of hydrodynamics and generate a family of non-stationary geodesics of the L2 metric in the volume preserving diffeomorphism group of S2. Restricting to a particular subset of Rossby-Haurwitz waves, this article shows that under certain conditions on the physical characteristics of the waves each

The objective of the present research article is to examine the behavior of spacetime with content of matter having magnetism say relativistic magneto-fluid spacetime. We discuss some geometrical properties of relativistic magneto-fluid spacetime. Next, we assume the relativistic magneto-fluid spacetime with Codazzi type and Ricci cyclic type matter tensor and study various results. In addition, we

We define ϕ-enveloids for one-parameter families of spherical Legendre curves. The ϕ-enveloids are not only the generalizations of isogonal trajectories of regular spherical curves but also the generalizations of envelopes of spherical curves. We also consider the relationships between enveloids of spherical Legendre curves and plane Legendre curves. Furthermore, we generalize the notions of involutes

Soliton solutions, lump solutions, breather solutions and soliton molecules are hot topics in recent years. And soliton molecules have been successfully discovered in optical experiments. In this paper, we firstly use the Hirota bilinear method to obtain the multiple solitary wave solutions of the (3+1)-dimensional Jimbo-Miwa equation. Secondly, on the basis of soliton solutions, the soliton molecule

Motivated by some computations of Feynman integrals and certain conjectures on mixed Tate motives, Bejleri and Marcolli posed questions about the F1-structure (in the sense of torification) on the complement of a hyperplane arrangement, especially for an arrangement defined in the space of cycles of a graph. In this paper, we prove that an arrangement has an F1-structure if and only if it is Boolean

We propose a generalization of the momentum map on a symplectic manifold with a Lie algebra action to a Courant algebroid structure. The theory of a momentum section on a Lie algebroid is generalized to the theory compatible with a Courant algebroid. As an example, we identify the momentum section in a constrained Hamiltonian mechanics with Courant algebroid symmetry. Moreover, we construct cohomological

Motivated by Wigner's theorem, a canonical construction is described that produces an Atiyah-Singer Dirac operator with both unitary and anti-unitary symmetries. This Dirac operator includes the Dirac operator for KR-theory as a special case, filling a long-standing gap in the literature. In order to make the construction, orientifold Spinc-structures are defined and classified using semi-equivariant

In this manuscript, we firstly suggest different type for Fermi-Walker transportations along with flow lines of a non-vanishing vector field in Minkowski spacetime. Moreover, we construct the evolution equations of Frenet fields by Fermi-Walker derivative in Minkowski spacetime. Also, Fermi Walker parallelism is obtained the evolution equations of Frenet fields. Finally, we obtain some new results

We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and connections in DPBs are investigated.

We study the Hull-Strominger system and the Anomaly flow on a special class of 2-step solvmanifolds, namely the class of almost-abelian Lie groups. In this setting, we characterize the existence of invariant solutions to the Hull-Strominger system with respect to the family of Gauduchon connections in the anomaly cancellation equation. Then, motivated by the results on the Anomaly flow, we investigate

We consider a certain super extension, called the super tau-cover, of a bihamiltonian integrable hierarchy which contains the Hamiltonian structures including both the local and non-local ones as odd flows. In particular, we construct the super tau-cover of the principal hierarchy associated with an arbitrary Frobenius manifold, and the super tau-cover of the Korteweg-de Vries (KdV) hierarchy. We also

On a complex manifold (M,J), we interpret complex symplectic and pseudo-Kähler structures as symplectic forms with respect to which J is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on 4-dimensional Lie algebras. We develop a method for constructing hypersymplectic structures from the above data. This allows us to obtain two families of hypersymplectic structures

A new super-exceptional embedding construction of the heterotic M5-brane's sigma-model was recently shown to produce, at leading order in the super-exceptional vielbein components, the super-Nambu-Goto (Green-Schwarz-type) Lagrangian for the embedding fields plus the Perry-Schwarz Lagrangian for the free abelian self-dual higher gauge field. Beyond that, further fields and interactions emerge in the

In this paper we consider the so-called twisted Heisenberg superalgebras over the complex number field, which are defined by adding derivations to Heisenberg superalgebras. By introducing the concept of blocks of type I, II and III for a Lie superalgebra, we classify the fine gradings up to equivalence on the twisted Heisenberg superalgebras and determine the Weyl groups of those gradings.

In this paper, we consider an Einstein-type equation on contact metric manifolds. First, we prove that any K-contact manifold admitting an Einstein-type metric is isometric to a unit sphere. Similar conclusion also holds for a contact metric manifold admitting an Einstein type metric with zero radial Weyl curvature and satisfying a commutativity condition. Finally, we study an Einstein-type equation

In this paper, we first introduce semi-symmetric metric and semi-symmetric non-metric connections on a n-distribution D of a (n+p)-dimensional semi-Riemannian manifold (M,g). Then we obtain the Gauss equations and the sectional curvature with respect to these connections. Finally, we give an example of a semi-Riemannian manifold with semi-symmetric metric and non-metric connections.

In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. In this second part, we shall adapt the

The lump solutions have been shown to be one of the most effective solutions for nonlinear evolution problems. The resilient Hirota bilinear method is used to evaluate the integrable (3+1)-dimensional nonlinear evolution equation in this work. For the problem under scrutiny, we establish novel types of solutions such as breather wave, lump-periodic, and two wave solutions. For easy observation, the

The study of warped products plays versatile roles in differential geometry as well as in mathematical physics, especially in general relativity (GR). In the present paper, we study statistical submanifolds in a statistical warped product with some related examples. For such submanifolds, we establish a Chen's first inequality and also discuss the equality case. Finally, we study the statistical warped

In this paper, we define and study two new structures on a differentiable manifold called by us an f(a,b)(3,2,1)-structure and a framed f(a,b)(3,2,1)-structure as a generalization of some geometric structures determined by polynomial structures, where a,b∈R and b≠0. At beginning, we present some examples regarding f(a,b)(3,2,1)-structures and establish their some fundamental properties. We also give

We construct an explicit family of irreducible representations of the canonical commutation relations parametrized by the space of pairs of transverse Lagrangian subspaces in the complexification of a symplectic vector space. We identify different restrictions of this family with previously studied families of Lion-Vergne, Satake, Grossmann, and Mumford. The classical Schrödinger and Fock-Segal-Bargmann

In this paper, we construct and study a new class of modules over the Block algebra B(q), where q is a nonzero complex number. We determine the irreducibilities of these modules and the isomorphisms among them. We also show that these modules exhaust all U(h)-free B(q)-modules of rank-1.

The present paper is devoted to generalized Sasakian space forms admitting conformal Ricci soliton and Quasi-Yamabe soliton. Nature of the conformal Ricci soliton is characterized on generalized Sasakian space form with various types of the potential vector field, and conditions for the conformal Ricci soliton to be shrinking, steady, or expanding are also given. Then it is shown that, depending on

We propose a notion of functor of points for noncommutative spaces, valued in categories of bimodules, and endowed with an action functional determined by a notion of hermitian structures and height functions, modeled on an interpretation of the classical functor of points as a physical sigma model. We discuss different choices of such height functions, based on different notions of volumes and traces

We carry out the extended symmetry analysis of a two-dimensional degenerate Burgers equation. Its complete point-symmetry group is found using the algebraic method, and all its generalized symmetries are proved equivalent to its Lie symmetries. We also prove that the space of conservation laws of this equation is infinite-dimensional and is naturally isomorphic to the solution space of the (1+1)-dimensional

We define Lagrangian Floer cohomology over Z2-coefficients by counting pearly trajectories for graded, exact Lagrangian immersions that satisfy a certain positivity condition on the index of the non-embedded points, and show that it is an invariant of the Lagrangian immersion under Hamiltonian deformations. We also show that it is naturally isomorphic to the Hamiltonian perturbed version of Lagrangian

Fractional differential equations play an essential role in describing the shallow water wave phenomena. In this article, we discussed the coupled Burgers-type equations in the sense of the fractional derivative of Riemann-Liouville. In return, a series of new results of this considered models, were obtained. In the first place, the formulation of the time fractional coupled Burgers-type equations

We review noncommutative Poisson structures on affine and projective spaces over C. We also construct a class of examples of noncommutative Poisson structures on CPn−1 for n>2. These noncommutative Poisson structures depend on a modular parameter τ∈C and an additional discrete parameter k∈Z, where 1≤k

In the present paper, first, resonant multi-soliton solutions of a combined pKP-BKP equation were obtained by carrying out the linear superposition principle and a group of 3D and contour images vividly represent the process of wave motion with physical interpretation. Next, M-breather solutions including 1-breather, 2-breather, 3-breather and hybrid solutions between breather and soliton have been

In this note we study a positivity notion for the curvature of the Bismut connection; more precisely, we study the notion of Bismut-Griffiths-positivity for complex Hermitian non-Kähler manifolds. Since the Kähler-Ricci flow preserves and regularizes the usual Griffiths positivity we investigate the behaviour of the Bismut-Griffiths-positivity under the action of the Hermitian curvature flows. In particular

Belavin-Polyakov solitons and topological loops for a polaritonic, i.e. two component coherent field in two dimensions have been studied under conformality constraint. The role of interactions is elucidated. Solitonic solutions of coupled non-linear equations have been calculated in frame of this study. Homogeneous and inhomogeneous phases are found for pseudospin respected different onsets. Polarization

In this paper, we construct the complex associated to an overdetermined system of PDE of order one with constant coefficients using the theory of exterior differential system of Cartan (see [1]). We show that if the tableau associated to the system of PDE is in involution then the complex contains only operators of order one given by the successive torsions of the system (see section 2 for the details)

The aim of this article is to investigate the uniqueness of solution of an inverse source problem for a generalized kinetic equation on a Riemannian manifold. The problem is related with an integral geometry problem in semi-geodesic coordinates. We prove the uniqueness in a convex domain by the help of Riemannian coordinates.

In this paper, we study Riemannian maps whose total manifolds admit a Ricci soliton and give a non-trivial example of such Riemannian maps. We obtain necessary conditions for any fiber of such Riemannian map to be Ricci soliton, almost Ricci soliton and Einstein. We also obtain necessary conditions for the range space of such Riemannian map to be Ricci soliton and Einstein. Further, we calculate scalar

It is shown that, if the energy in the Schwarzian mechanics (SM) is equal to the coupling constant in the de Alfaro-Fubini-Furlan (dAFF) model, there exists a link between these two systems. In particular, the equation of motion, sl(2,R)-symmetry transformations and the corresponding conserved charges of SM can be derived from those of dAFF model by applying a coordinate transformation of a special

In this paper, we investigate the extended Caudrey–Dodd–Gibbon equation. Using N-soliton solution and a novel velocity resonance condition can generate soliton molecules of the extended Caudrey–Dodd–Gibbon equation. Further, by changing the distance between two solitons in a soliton molecule, each single soliton molecule can transform an asymmetric soliton. Also, we observed the collision between one

We give necessary and sufficient conditions for the complete integrability of first order N–dimensional differential systems. We propose a new method to determine in the Jacobi Theorem the last N−1 first integral for the complete integrability of an N–dimensional differential system with N−2 independent first integrals and with a Jacobi multiplier. As an application we study the complete integrability

In this paper, we define the evolutoids and the pedaloids of a spacelike curve on a spacelike surface in Minkowski 3-space. Firstly, considering the situation in the circle and using a moving frame along the curve, we obtain that the evolutoids of the spacelike curves on the spacelike surface is expressed with ruled surfaces. Moreover, we investigate relationships between the pedal surfaces of the

By studying Rozansky-Witten theory with non-compact target spaces we find new connections with knot invariants whose physical interpretation was not known. This opens up several new avenues, which include a new formulation of q-series invariants of 3-manifolds in terms of affine Grassmannians and a generalization of Akutsu-Deguchi-Ohtsuki knot invariants.

We determine a formula to compute the defining function of a gradient almost Ricci-Bourguignon soliton by means of the potential vector field, providing in this sense two examples. We also give a rigidity result in this case. Moreover, we deduce some curvature properties of solitons with torse-forming potential vector field. Further we generalize some of the results to almost η-Ricci-Bourguignon solitons

In this paper, we study the well-known unicorn problem for Finsler metrics. First, we prove that every homogeneous Landsberg surface has isotropic flag curvature. Then by using this particular form of the flag curvature, we prove a rigidity result on the homogeneous Landsberg surfaces. Indeed, we prove that every homogeneous Landsberg surface is Riemannian or locally Minkowskian. Thus, we give an affirmative

Under investigation in this paper is the generalized (2+1)-dimensional Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation. Based on the bilinear Hirota method, the M-lump solution and N-soliton solution are constructed by giving some special activation functions in the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue waves are obtained with the aid

In many physical situations, variable-coefficient nonlinear partial differential equations provide us with more realistic aspects of media inhomogeneities and boundary nonuniformities than constant-coefficient. In this research, we extract some new structures of lump solutions to some important nonlinear equations with variable coefficients. The equations under consideration are the (2+1)-dimensional

We classify finite energy harmonic 2-forms on the asymptotically flat gravitational instanton constructed by Chen and Teo. We prove that every U(1)-bundle admits a unique anti-self-dual Yang-Mills instanton (up to gauge equivalence) which we describe explicitly in coordinates. As an application, we compute the classical contribution to partition function for Maxwell theory with theta term.

A generalization of Ricci-like solitons with torse-forming potential, which is constant multiple of the Reeb vector field, is studied. The conditions under which these solitons are equivalent to almost Einstein-like metrics are given. Some results are obtained for a parallel symmetric second-order covariant tensor. Finally, an explicit example of an arbitrary dimension is given and some of the results

In [13], [17] and [29], we introduced the category of colored supermanifolds (Z2n-supermanifolds or just Z2n-manifolds (Z2n=Z2×…×Z2 (n times))), explicitly described the corresponding Z2n-Berezinian and gave first insights into Z2n-integration theory. The present paper contains a detailed account of parts of the Z2n-differential calculus and of the Z2n-variants of the trilogy of local theorems, which

For the double complex structure of grading-restricted vertex algebra cohomology defined in [6], [7], we introduce a multiplication of elements of double complex spaces. We show that the orthogonality and bi-grading conditions applied on double complex spaces, provide in relation among mappings and actions of co-boundary operators. Thus, we endow the double complex spaces with structure of bi-graded