arXiv research

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

Survey of recent results in weak almost contact structures.

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

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

Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu 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 weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.

The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.

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.

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

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 …

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

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

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.

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…

Study explores weak generalized K-contact structures in contact metric spaces.

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…

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

Study on $G_2^*$ structures and almost para-contact structures in 7D.

The study of harmonicity for almost contact metric structures was initiated by Vergara-Díaz and Wood and continued by González-Dávila and the present author. By using the intrinsic torsion and some restriction on the type of almost contact metric structure, González-Dávila and the present author have characterised harm…

Study harmonicity of normal almost contact structures on Riemannian manifolds.

New structures defined for studying contact foliations and their geometry.

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…

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

We study almost contact metric structures induced by 2-fold vector cross products on manifolds with $G_2$ structures. We get some results on possible classes of almost contact metric structures. Finally we give examples.

We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the structure of a Lie algebra. We describe Lie subalgebras in this Lie algebra given by…

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…

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

An almost contact metric structure is parametrized by a section of an associated homogeneous fibre bundle, and conditions for this to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field, and the almost complex structure in the contact subbundle. Several examples are giv…

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

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…

We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point of the generalized almost contact structures. We obtain a generalized Sasakian structure on a non-compact manifold which…

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

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…

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…

On a manifold with an almost contact metric structure $(\varphi,\vecξ,η,g,X,D)$ the notions of the interior and the $N$-prolonged connections are introduced. Using the $N$-prolonged connection, a new almost contact metric structure is defined on the distribution $D$. The properties of this structure are studied.

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

We study almost bi-paracontact structures on contact manifolds. We prove that if an almost bi-paracontact structure is defined on a contact manifold $(M,η)$, then under some natural assumptions of integrability, $M$ carries two transverse bi-Legendrian structures. Conversely, if two transverse bi-Legendrian structures …

In this paper, left-invariant almost contact metric structures on three-dimensional non-unimodular Lie groups are investigated. It is proved that for every Riemannian Lie group, there is one of these structures. In addition, left-invariant normal almost contact metric structures on three dimensional non-unimodular Lie …

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

The notions of a twistor space of a contact manifold and a contact connection on such a manifold have been introduced by L. Vezzoni as extensions of the corresponding notions in the case of a symplectic manifold. Given a contact connection on a contact manifold one can define an almost $CR$-structure on its twistor spa…

Study new warped product metric in contact geometry.

We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of the Riemann curvature tensor and find conditions relating the harmonicity of the a…

Simplified construction of contact triad connection for analysis.