On semi-Quasi-Einstein Manifold

TL;DR

This paper introduces semi-quasi-Einstein manifolds with semi-symmetric metric connections, demonstrating that well-known spacetimes like Schwarzschild and Kottler possess this structure, and explores related curvature conditions.

Contribution

It defines semi-quasi-Einstein manifolds with semi-symmetric metric connections and shows their presence in classical spacetimes, expanding the understanding of their geometric properties.

Findings

Schwarzschild and Kottler spacetimes are semi-quasi-Einstein.

Curvature conditions are studied in these manifolds.

The structure generalizes Einstein manifolds with semi-symmetric connections.

Abstract

In the present paper we introduce a semi-quasi-Einstein manifold from a semi symmetric metric connection. Among others, the popular Schwarzschild and Kottler spacetimes are shown to possess this structure. Certain curvature conditions are studied in such a manifold with a Killing generator.