arXiv research

Survey of recent results in weak almost contact structures.

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

Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.

Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.

New structure with B-metric extends classical almost contact structures.

New metric structures generalize Sasakian and cosymplectic structures, proving rigidity and finding conditions.

The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.

Study on a new type of manifolds that generalize almost C-manifolds.

The paper studies a new structure on contact manifolds and its foliation properties.

The paper explores generalized Riemannian manifolds with weak metric structures.

Study curvature properties of w.a. S-manifolds with new conditions.

We continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost contact manifolds to which there is a Stein cobordism from any other (2q+1)-dimensional contact manifold. We show that the product M x S^2 …

The paper presents the Einstein connection for nonsymmetric pseudo-Riemannian manifolds.

We study weakened $f$-structures on manifolds, generalizing classical results.

The paper explores new connections in non-symmetrical gravitational theory using weak metric structures.

The study explores new metric structures on manifolds, linking them to Einstein metrics.

Study weak $f$-K-contact manifolds, finding Einstein-type metrics and solitons.

We study weak versus strong symplectic fillability of some tight contact structures on torus bundles over the circle. In particular, we prove that almost all of these tight contact structures are weakly, but not strongly symplectically fillable. For the 3-torus this theorem was established by Eliashberg.

The author is planning if possible classify all three-dimensional $(κ,μ)$-manifolds wether contact metric, almost cosymplectic, para-contact metric, almost para-cosymplectic. Of course classification in contact or almost cosymplectic cases already is provdied. Up to authors knowledge there is no classification for para…

In this article, we study an almost contact metric structure on a $G_2$-manifold constructed by Arikan, Cho and Salur in via the classification of almost contact metric structures given by Chinea and Gonzalez. In particular, we characterize when this almost contact metric structure is cosymplectic and narrow down the p…

The paper connects complex contact structures to specific types of almost contact 3-structures.

In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of almost contact metric spaces, more precisely, Hermitian almost contact metric spac…

Develops a diagrammatic method for symplectic filling classifications.

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced mani…

A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A canonical construction producing a Sasaki-like almost contact complex Riemannian ma…

The paper defines quasi-isometry for almost contact metric manifolds and explores its properties.

We give a characterization of a contact metric manifold as a special almost contact metric manifold and discuss an almost contact metric manifold which is {a} natural generalization of the contact metric manifolds introduced by Y. Tashiro.

Study harmonicity of normal almost contact structures on Riemannian manifolds.

Families of linear connections are constructed on almost contact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connection are studied on two basic cl…

The φ-sectional curvature of statistical structures on almost contact metric manifolds is always non-positive.

The paper defines $η$-normality for contact and paracontact manifolds and explores their properties.

Researchers extend Godbillon-Vey functional to almost contact manifolds, finding critical structures.

Study on harmonicity of maps between different types of almost contact metric manifolds.

We study harmonic almost contact structures in the context of contact metric manifolds, and an analysis is carried out when such a manifold fibres over an almost Hermitian manifold, as exemplified by the Boothby-Wang fibration. Two types of almost contact metric warped products are also studied, relating their harmonic…

In this paper, the notion of an almost contact Kählerian structure is introduced. The interior geometry of almost contact Kählerian spaces is investigated. On the zero-curvature distribution of an almost contact metric structure, as on the total space of a vector bundle, an almost contact Kählerian structure is obtaine…

New structures defined for studying contact foliations and their geometry.

Almost contact manifolds with B-metric are considered. A special linear connection is introduced, which preserves the almost contact B-metric structure on these manifolds. This connection is investigated on some classes of the considered manifolds.

Study new warped product metric in contact geometry.

Almost contact manifolds with B-metric are considered. Of special interest are the so-called vertical classes of the almost contact B-metric manifolds. Curvature properties of these manifolds are studied. An example of 5-dimensional manifolds is constructed and characterized.

This paper is devoted to the study of curvature and torsion of almost contact curves in trans-Sasakian 3-Manifolds. The conditions for the frenet curves to be almost contact curves in trans-Sasakian 3-manifolds have been obtained.

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

Simplified construction of contact triad connection for analysis.

In this paper, we introduce generalized almost para-contact manifolds and obtain normality conditions in terms of classical tensor fields. We show that such manifolds naturally carry certain Lie bialgebroid/quasi-Lie algebroid structures on them and we relate this new generalized manifolds with classical almost para-co…

We prove that every homotopy class of almost contact structures on a closed 5-dimensional manifold admits a contact structure.

On connected manifolds of dimension higher than three, the non-existence of $132$ Chinea and González-Dávila types of almost contact metric structures is proved. This is a consequence of some interrelations among components of the intrinsic torsion of an almost contact metric structure. Such interrelations allow to des…

These notes are intended to be an introduction to the use of approximately holomorphic techniques in almost contact and contact geometry. We develop the setup of the approximately holomorphic geometry. Once done, we sketch the existence of the two main geometric decompositions available for an almost contact or contact…

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

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. We classify these structures by their intrinsic torsion and review the literature in terms of this scheme. Moreover, we determine necessary and sufficient conditions for the existence of metric connections with vectorial, totally…