Related papers: Nullity distributions associated with Chern connec…

The aim of this paper is to introduce a cosymplectic analouge of conformal connection in a cosymplectic manifold and proved that if cosymplectic manifold M admits a cosymplectic conformal connection which is of zero curvature, then the…

On a smooth manifold with distributions ${\cal D}_1$ and ${\cal D}_2$ having trivial intersection, we consider the integral of their mutual curvature, as a functional of Riemannian metrics that make the distributions orthogonal. The mutual…

The first variant of this article contained a fatal error. Therefore, we publish second version our paper. In the present paper, we prove that the curvature operator of the second kind of a Riemannian manifold is strictly positive if its…

The present paper is devoted to the investigation of absolutely continuous curves in asymmetric metric spaces induced by Finsler structures. Firstly, for asymmetric spaces induced by Finsler manifolds, we show that three different kinds of…

We define integral geometric analogues of the Chern classes for real vector bundle on a smooth real variety. More precisely, we define the Chern densities of a real bundle. These densities are analogues of the Chern forms of a complex…

In this note it is shown that Berwald spaces admitting the same norm-preserving torsion-free affine connection have the same (weighted) Ricci curvatures. Combing this with Szab\'o's Berwald metrization theorem one can apply the…

We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface $\mathcal{Q}^n$ of dimension $n \geq 3$, and its twistor space $\mathbb{PT}$, defined to be the space of all linear…

We consider an almost complex manifold with Norden metric (i. e. a metric with respect to which the almost complex structure is an anti-isometry). On such a manifold we study a linear connection preserving the almost complex structure and…

For the non-rotating BTZ black hole, the distributional curvature tensor field is found. It is shown to have singular parts proportional to a $\delta$-distribution with support at the origin. This singularity is related, through Einstein…

A type of almost contact hypersurfaces with Norden metric of a Kaehler manifold with Norden metric is considered. The curvature tensor and the special sectional curvatures are characterized. The canonical connection on such manifolds is…

We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…

We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give…

We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show…

We use techniques based on the splitting tensor to explicitly integrate the Codazzi equation along the relative nullity distribution and express the second fundamental form in terms of the Jacobi tensor of the ambient space. This approach…

Finsler metrics are direct generalizations of Riemannian metrics such that the quadratic Riemannian indicatrices in the tangent spaces of a manifold are replaced by more general convex bodies as unit spheres. A linear connection on the base…

We introduce a class of null hypersurfaces of a semi-Riemannian manifold, namely, screen quasi-conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to…

We prove that in a Finsler manifold with vanishing $\chi$-curvature (in particular with constant flag curvature) some non-Riemannian geometric structures are geodesically invariant and hence they induce a set of non-Riemannian first…

In this paper, we prove the following two results: First, we study a class of conformally invariant operators $P$ and their related conformally invariant curvatures $Q$ on even-dimensional Riemannian manifolds. When the manifold is locally…

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities…

We consider closed manifolds that admit a metric locally isometric to a product of symmetric planes. For such manifolds, we prove that the Euler characteristic is an obstruction to the existence of flat structures, confirming an old…