Some Types of Weakly Ricci Symmetric Riemannian Manifolds

TL;DR

This paper investigates conditions under which certain weakly Ricci symmetric Riemannian manifolds exhibit specific curvature properties, expanding understanding of their geometric classifications in higher dimensions.

Contribution

It identifies criteria for weakly Ricci symmetric manifolds to be classified as quasi-Einstein, quasi-constant curvature, or hyper quasi-constant curvature.

Findings

Quasi-conformally flat weakly Ricci symmetric manifolds can be hyper quasi-constant curvature.

Pseudo projectively flat weakly Ricci symmetric manifolds can be pseudo-quasi constant curvature.

W2-flat weakly Ricci symmetric manifolds can be quasi-Einstein.

Abstract

In this paper we discuss when a quasi-conformally flat weakly Ricci symmetric manifold (of dimension greater than 3) becomes a manifold of hyper quasi-constant curvature, a quasi-Einstein manifold and a manifold of quasi-constant curvature. Also we discuss when a pseudo projectively flat weakly Ricci symmetric manifold (of dimension greater than 3) becomes pseudo-quasi constant curvature and a quasi-Einstein manifold, and when a W2-flat weakly Ricci symmetric manifold (of dimension greater than 3) becomes a quasi-Einstein manifold.