Some Types of Weakly Ricci Symmetric Riemannian Manifolds
Payel Karmakar, Arindam Bhattacharyya

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds
