arXiv research

The notion of generalized almost paracontact structure on the generalized tangent bundle $TM\oplus T^*M$ is introduced and its properties are investigated. The case when the manifold $M$ carries an almost paracontact metric structure is also discussed. Conditions for its transformed under a $β$- or a $B$-field transfor…

In this paper, we define almost paracontact and normal almost paracontact Finsler structures on a vector bundle and find some conditions for integrability of these structures. We define paracontact metric, para- Sasakian and K-paracontact Finsler structures and study some properties of these structures. For a K-paracon…

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 …

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

The goal of this paper, using lifting theory it is to produce almost paracomplex struc- tures on the tangent bundle of almost Lorentzian r-paracontact manifold endowed with almost Lorentzian r-paracontact structure. Finally, we discuss the effect over dynamics systems of the produced geometrical structures.

Study on hypersurfaces with specific geometric structures.

The paper explores new structures on cotangent bundles induced by natural Riemann extensions.

The paper reclassifies almost paracontact metric manifolds into 12 classes.

Study of 3D Lie group structures with special Riemannian properties.

New connections defined for a specific geometric structure.

The paper classifies 3D paracontact and almost paracosymplectic spaces.

The paper classifies hypersurfaces with parallel almost paracontact structures.

Study on specific types of Riemannian manifolds with detailed tensor analysis.

In this study, taking into considering lifting theory, we shall obtain both almost complex and paracomplex structures on the tangent bun- dle, based on almost Lorentzian r-contact and r-paracontact manifold.

Study on a specific type of Riemannian manifolds constructed from 2D space-forms.

Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and suffcient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that the normal almost paracontact …

Study on hyperspheres in 4-spaces as special Riemannian manifolds.

The paper constructs and classifies 3D Walker manifolds with specific structures.

Study of $η$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds.

The study explores δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds.

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

Study connects Lie groups to specific Riemannian manifolds.

The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold to be paraSasakian. A $\mathcal{D}$-homothetic transformation is determined as a special gauge transformation. The $η$-Einstein manifold are defined, it is prove that their scalar curvature is a …

In this paper eleven basic classes of almost paracontact manifolds are introduced and some examples are constructed.

The paper classifies geometric structures of δ-almost Yamabe solitons on paracontact metric manifolds.

In this paper we define and study the slant and semi-slant submanifolds of a Lorentzian almost paracontact manifold. Some necessary and sufficient conditions for a submanifold of a Lorentzian almost paracontact manifold to be slant are obtained. We give some examples for the slant and semi-slant submanifolds of a Loren…

In this paper, we study the invariant and noninvariant hypersurfaces of (1,1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an (1,1,1) almost contact manifold admits an almost product structure. We in…

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

In monograph of D. E. Blair "Riemannian geometry of contact and symplectic manifolds" and in the paper of S. Zamkovoy "Canonical connections on paracontact manifolds", the curvature identities respectively for contact and paracontact metric manifold are proved. We obtain the curvature identity in the wider class of man…

We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.

The presented paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non- Frenet slant curves (with null tangents or null normals) are obtained. The achieved results are illustrated by ex…

Our aim in this paper is to give some examples of $(a, 1)f$ Riemannian structures (a generalization of an $r$-paracontact structure) induced on product of spheres of codimension $r$ ($r \in \{1,2\}$) in an $m$-dimensional Euclidean space ($m>2$), endowed with an almost product structure.

We construct a metrical framed structure on the tensor bundle of a Riemannian manifold equipped with a Cheeger-Gromoll type metric and by restricting this structure to the tensor sphere bundle, we obtain an almost metrical paracontact structure on the tensor sphere bundle. Moreover, we show that the tensor sphere bundl…

Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,\langle,\rangle)$, we construct a family of paracontact metric structures. We prove that this class of paracontact metric structures is invariant under $\mathcal D$-homothetic…

We study the interplays between paracontact geometry and the theory of bi-Legendrian manifolds. We interpret the bi-Legendrian connection of a bi-Legendrian manifold M as the paracontact connection of a canonical paracontact structure induced on M and then we discuss many consequences of this result both for bi-Legendr…

In this paper we introduce the concept of $(\varepsilon)$-almost paracontact manifolds, and in particular, of $(\varepsilon)$-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of $(\varepsilon)$-para Sasakian manifolds are obtained. We prove that if a…

In this paper, we initiate the study of lightlike hypersurfaces of an $(ε)$-almost paracontact metric manifold which are tangent to the structure vector field. In particular, we give definitions of invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, and give some examples. Integrability…

In this paper we study slant submanifolds of Lorentzian almost contact manifolds. We have taken the submanifold as a space like and then defined the slant angle on a submanifold and thus we extended the results of A. Lotta (Slant submanifolds in contact geometry [8]) and M. A. Khan et. al. (Slant submanifolds of Lorent…

A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric of neutral signature if and only if the pc conformal curvature vanishes. I…

We prove that any contact metric $(κ,μ)$-space $(M,ξ,φ,η,g)$ admits a canonical paracontact metric structure which is compatible with the contact form $η$. We study such canonical paracontact structure, proving that it verifies a nullity condition and induces on the underlying contact manifold $(M,η)$ a sequence of com…

Study classifies metrics on anti-de Sitter spacetime with specific symmetries.

Study the geometry of weak para-f-structures and subclasses.

An example of a three dimensional flat paracontact metric manifold with respect to Levi-Civita connection is constructed. It is shown that no such manifold exists for odd dimensions greater than or equal to five.

Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT with torsion) are considered. It is shown that an almost Hermitian manifold is an NGT with torsion if and only if it is a Nearly Kähler manifold. In the case of an almost contact metric manifo…

We introduce and study $H$-paracontact metric manifolds, that is, paracontact metric manifolds whose Reeb vector field $ξ$ is harmonic. We prove that they are characterized by the condition that $ξ$ is a Ricci eigenvector. We then investigate how harmonicity of the Reeb vector field $ξ$ of a paracontact metric manifold…

Study revises results on a specific type of 3D paracontact metric manifolds.

Study classifies 3D paracontact manifolds based on curvature properties.

We completely describe paracontact metric three-manifolds whose Reeb vector field satisfies the Ricci soliton equation. While contact Riemannian (or Lorentz\-ian) Ricci solitons are necessarily trivial, that is, $K$-contact and Einstein, the paracontact metric case allows nontrivial examples. Both homogeneous and inhom…