A classification of conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds

TL;DR

This paper classifies conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent structure, showing they are either de Sitter or anti-de Sitter spaces, with implications for spacetime models.

Contribution

It provides a complete classification of conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds, identifying them as de Sitter or anti-de Sitter spaces.

Findings

Conformally flat generalized Ricci recurrent manifolds are either de Sitter or anti-de Sitter.

Such manifolds in spacetime context are restricted to de Sitter or anti-de Sitter spacetimes.

The classification simplifies understanding of these geometric structures.

Abstract

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, $(GR)_n$ structure are completely classified in this short report. A conformally flat generalized Ricci recurrent pseudo-Riemannian manifold is shown to be either a de Sitter space or an anti-de Sitter space. In particular, a conformally flat generalized Ricci recurrent spacetime must be either a de Sitter spacetime or an anti-de Sitter spacetime.