arXiv research

Cosymplectic geometry can be viewed as an odd dimensional counterpart of symplectic geometry. Likely in the symplectic case, a related property which is preservation of closed forms $ω$ and $η$, refers to the theoretical possibility of further understanding a cosymplectic manifold $(M, ω, η)$ from its group of diffeomo…

Extends integrability to cosymplectic manifolds.

The paper explores similarities in even and odd-dimensional geometry.

Researchers tackle the globalization problem of locally cosymplectic Hamiltonian dynamics.

Infinite-dimensional contact geometry explored.

We obtain a generalization of the Kodaira-Morrow stability theorem for cosymplectic structures. We investigate cosymplectic geometry on Lie groups and on their compact quotients by uniform discrete subgroups. In this way we show that a compact solvmanifold admits a cosymplectic structure if and only if it is a finite q…

In the paper we develop a framework for the alternative way of the study of a local geometry of almost cosymplectic manifolds with Kahlerian leaves. The main idea is to apply the concept of a geometry and analysis of CR manifolds. Locally the almost cosymplectic manifold is modeled on the 'mixed' space RxCn. There is g…

We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.

This paper extends symplectic reduction to cosymplectic groupoids and explores their properties.

New method for studying $t$-dependent Hamilton equations on cosymplectic manifolds.

New geometric structures defined in contact metric geometry.

New geometric structures on 3-manifolds discovered and proven for all closed orientable ones.

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.

We review topological properties of Kähler and symplectic manifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the $b_1=1$ c…

The Navier-Stokes equations on certain manifolds can perform universal computation.

The study examines conditions for weak nearly cosymplectic manifolds to split into products.

The paper extends Vlasov kinetic theory to time-dependent dynamics using cosymplectic and cocontact manifolds.

In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems. In particular, we generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3D systems. We illustrate our cons…

The paper extends Marsden-Weinstein reduction to mechanical presymplectic structures for time-dependent Hamiltonian systems.

In [21], the authors initiated the study of quasi generalized CR (QGCR)-null submanifolds. In this paper, attention is drawn to some distributions on ascreen QGCR-null submanifolds in an indefinite nearly cosymplectic manifold. We characterize totally umbilical and irrotational ascreen QGCR-null submanifolds. We finall…

Extends coisotropic embedding theorem to various geometric settings.

The study classifies h-almost Ricci-Yamabe solitons in various paracontact manifolds.

3-quasi-Sasakian manifolds were studied systematically by the authors in a recent paper as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. This paper throws new light on their geometric structure which reveals to be generally richer compared to the 3-Sasakian subclass. In fact, it turns out that t…

Study on cosymplectic groupoids with structural results.

We completely characterize cosymplectic and $α$-cosymplectic Lie algebras in terms of corresponding symplectic Lie algebras and suitable derivations on them. Several examples are given and classification results are obtained in dimension five for cosymplectic, $K$-cosymplectic and coKähler Lie algebras.

Paper defines cosymplectic conformal connections and shows their curvature implications.

We introduce cosymplectic circles and cosymplectic spheres, which are the analogues in the cosymplectic setting of contact circles and contact spheres. We provide a complete classification of compact 3-manifolds that admit a cosymplectic circle. The properties of tautness and roundness for a cosymplectic $p$-sphere are…

Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant s…

In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(κ,μ)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl structures. Next for a three dimensional compact almost $α$-cosymplectic manifol…

In this article we study an almost $f$-cosymplectic manifold admitting a Ricci soliton. We first prove that there do not exist Ricci solitons on an almost cosymplectic $(κ,μ)$-manifold. Further, we consider an almost $f$-cosymplectic manifold admitting a Ricci soliton whose potential vector field is the Reeb vector fie…

3-quasi-Sasakian manifolds were recently studied by the authors as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. In this paper some geometric properties of this class of almost 3-contact metric manifolds are briefly reviewed, with an emphasis on those more related to physical applications.

Improves Marsden-Weinstein reduction theory for k-polysymplectic manifolds.

In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemannian metric. These structures generalize coKähler structures, in the same way as K-contact structures generalize Sasakian structures. In analogy to the contact case, we dis…

New geometric framework for non-conservative field theories with time-dependent terms.

Generalizes symplectic reduction to cosymplectic groupoid actions.

The paper classifies cosymplectic manifolds with critical metrics in dimension 3.

The paper derives Chen inequalities for statistical submanifolds in cosymplectic manifolds.

Study on solitons in complex Riemannian manifolds with specific properties.

Recently, we have shown that there do not exist the warped product semi-slant submanifolds of cosymplectic manifolds [10]. As nearly cosymplectic structure generalizes cosymplectic ones same as nearly Kaehler generalizes Kaehler structure in almost Hermitian setting. It is interesting that the warped product semi-slant…

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a corollary for the almost cosymplectic statistical manifold with Kaehler leaves. We a…

For a finite family of 3-dimensional almost contact metric manifolds with closed the structure form $η$ is described a construction of an almost contact metric manifold, where the members of the family are building blocks - cells. Obtained manifold share many properties of cells. One of the more important are nullity c…

New theory for Hamiltonian actions on special geometric structures.

The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class of gradient Ricci solitons, for which we give the local classificatio…

In this article, we study almost cosymplectic manifolds admitting quasi-Einstein structures $(g, V, m, λ)$. First we prove that an almost cosymplectic $(κ,μ)$-manifold is locally isomorphic to a Lie group if $(g, V, m, λ)$ is closed and on a compact almost $(κ,μ)$-cosymplectic manifold there do not exist quasi-Einstein…

The paper explores conditions for manifolds to have specific geometric structures.

We continue the program of Chinea, De Leon and Marrero who studied the topology of cosymplectic manifolds. We study 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kaehler structures. We show that there is an action of the Lie algebra so(4,1) on the basic cohomology spaces of a compact …

Main interest of the present paper is to investigate the almost α-cosymplectic manifolds for which the characteristic vector field of the almost α-cosymplectic structure satisfies a specific (κ,μ,ν)-nullity condition. This condition is invariant under D-homothetic deformation of the almost cosymplectic (κ,μ,ν)-spaces i…

Abstract: Study Hamiltonian systems on almost cosymplectic manifolds, extending contact Hamiltonian systems.