Related papers: On $(N(k),\xi)$-semi-Riemannian manifolds: Semisym…

The present paper deals with the proper existence of a generalized class of recurrent manifolds, namely, hyper-generalized recurrent manifolds. We have established the proper existence of various generalized notions of recurrent manifolds.…

In this article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric 2-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and…

The main object of the present paper is to study the geometric properties of a generalized Roter type semi-Riemannian manifold, which arose in the way of generalization to find the form of the Riemann-Christoffel curvature tensor $R$. Again…

In this paper, we study two notions of rigidity, one of conformal submersions and the other of quasi Einstein manifolds, with an attempt to relate the two notions. Note that a smooth submersion between Riemannian manifolds is called…

The aim of the present paper to define and study semi-slant $\xi^\perp-$Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant $\xi^\perp-$Riemannian submersions, semi-invariant…

Let F be a Riemannian submersion from an almost Hermitian manifold (M; gM; J) onto a Riemannian manifold (N; gN). We introduce the notion of the semi-slant submersion. And then we obtain some properties about it. In particular, we give some…

A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose fourth power is the identity, is considered. This structure acts as an isometry with respect to the metric. A Riemannian almost product manifold…

This research work introduces the structure of invariant and screen semi-invariant lightlike submanifolds of a metallic semi-Riemannian manifold with a quarter symmetric non-metric connection, elaborated with examples. It delves into the…

We introduce the notion of a semi-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of semi-Riemannian manifolds within a noncommutative setting. It turns out that the relevant spaces in…

As a generalization of slant submersions (Sahin, 2011), semi-slant submersions (Park and Prasad), and slant Riemannian maps (Sahin), we define the notion of semi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds.…

Let F be a Riemannian submersion from an almost Hermitian manifold (M; gM; J) onto a Riemannian manifold (N; gN). We introduce the notion of the v-semi-slant submersion. And then we obtain some properties on it. In particular, we give some…

In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metric connection on super warped product spaces. Next, we…

For any semi-Riemannian manifold (M,g) we define some generalized curvature tensor as a linear combination of Kulkarni-Nomizu products formed by the metric tensor, the Ricci tensor and its square of given manifold. That tensor is closely…

In this paper, we define the semi-symmetric metric connection on super Riemannian manifolds. We compute the semi-symmetric metric connection and its curvature tensor and its Ricci tensor on super warped product spaces. We introduce two kind…

Curvature properties of a metric connection with totally skew-symmetric torsion are investigated. It is shown that if either the 3-form $T$ is harmonic, $dT=\delta T=0$ or the curvature of the torsion connection $R\in S^2\Lambda^2$ then the…

This text is an introductory review of the basic concepts of the theory of semi-Riemannian geometry on real finite-dimensional manifolds without boundary.

The paper will study a new quarter-symmetric non-metric connection on a generalized Riemannian manifold. It will determine the relations that the torsion tensor satisfies. The exterior derivative of the skew-symmetric part $F$ of basic…

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold $M$, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is…

We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.

Every Heisenberg manifold has a natural "sub-Riemannian" metric with interesting properties. We describe the corresponding noncommutative metric structure for Rieffel's quantum Heisenberg manifolds.