English

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

Differential Geometry 2021-11-30 v1

Abstract

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, (GR)n(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.

Keywords

Cite

@article{arxiv.2107.05389,
  title  = {A classification of conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds},
  author = {Avik De and Loo-Tee How},
  journal= {arXiv preprint arXiv:2107.05389},
  year   = {2021}
}