Related papers: Almost Paracontact Finsler Structures on Vector Bu…

On a sub-Riemannian manifold, a connection with skew-symmetric torsion is defined as the unique connection from the class of $N$-connections that has this property. Two cases are considered separately: sub-Riemannian structure of even rank,…

In this paper, a frame is introduced on tangent bundle of a Finsler manifold in a manner that it makes some simplicity to study the properties of the natural foliations in tangent bundle. Moreover, we show that the indicatrix bundle of a…

We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor $\psi$ of algebraic type $F \cdot \psi = 0$ with respect to the unique connection $\nabla$ preserving the quasi-Sasakian structure and…

The purpose of this paper is to study the Sasakian geometry on odd dimensional sphere bundles over a smooth projective algebraic variety $N$ with the ultimate, but probably unachievable goal of understanding the existence and non-existence…

For an almost contact metric manifold $N$, we find conditions for which either the total space of an $S^1$-bundle over $N$ or the Riemannian cone over $N$ admits a strong K\"ahler with torsion (SKT) structure. In this way we construct new…

In this article, we consider the almost Hermitian structure on $TM$ induced by a pair of a metric and an affine connection on $M$. We find the conditions under which $TM$ admits almost K\"ahler structures, K\"ahler structures and Einstein…

The paper is a complete study of paracontact metric manifolds for which the Reeb vector field of the underlying contact structure satisfies a nullity condition (the condition \eqref{paranullity} below, for some real numbers $% \tilde\kappa$…

In this paper, the notion of an almost contact K\"ahlerian structure is introduced. The interior geometry of almost contact K\"ahlerian spaces is investigated. On the zero-curvature distribution of an almost contact metric structure, as on…

We carry on a systematic study of nearly Sasakian manifolds. We prove that any nearly Sasakian manifold admits two types of integrable distributions with totally geodesic leaves which are, respectively, Sasakian or $5$-dimensional nearly…

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. In particular, we generalize the class of quasi-Sasaki manifolds and characterize these structures by their intrinsic torsion. Among other things, we…

We investigate 7 dimensional almost para-contact metric structures induced by the 3-forms of $G_2^*$ Structures. We calculate the projections that determine to which class the almost para-contact structure belongs, by using the properties…

Let $(M,g)$ be an n-dimensional Riemannian manifold and $T^{*}M$ be its cotangent bundle equipped with a Riemannian metric of Cheeger Gromoll type which rescale the horizontal part by a nonzero differentiable function. The main purpose of…

The nearly K\"{a}hler structures on the 6-sphere, as a twistor bundle sections are researched. We show that for any point of twistor bundle there exists an 1-parametric family of sections, passing through the point, which give nearly…

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…

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation…

Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact…

In this article, we introduce some metallic structures on the tangent bundle of a P-Sasakian manifold by complete lift, horizontal lift and vertical lift of a P-Sasakian structure $(\phi, \eta,\xi)$ on tangent bundle. Then we investigate…

In this paper, we define vector bundles within the framework of almost mathematics (referred to as almost vector bundles) and establish the $v$-descent theorem together with a structure theorem for these bundles over perfectoid spaces. The…

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

All invariant contact metric structures on tangent sphere bundles of each compact rank-one symmetric space are obtained explicitly, distinguishing for the orthogonal case those that are K-contact, Sasakian or 3-Sasakian. Only the tangent…