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

Avik De; Loo-Tee How

doi:10.1142/s0219887822500232

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arXiv · 2107.05389

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

Avik De·Loo-Tee How

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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.

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Avik De, Loo-Tee How. 2021-07-08. A classification of conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds. https://doi.org/10.1142/s0219887822500232

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