On Conformally Symmetric Generalized Ricci-Recurrent Manifolds with applications in general relativity

YILMAZ H.

BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.13, no.3, pp.39-50, 2021 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 3
  • Publication Date: 2021
  • Journal Name: BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.39-50
  • Keywords: Generalized Ricci-recurrent manifold, Quasi-Einstein manifold, Perfect fluid spacetime, Einstein's field equation, Energy-momentum tensor
  • Marmara University Affiliated: Yes

Abstract

In this paper, we consider conformally symmetric generalized Ricci recurrent manifolds. We prove that such a manifold is a quasi-Einstein manifold and study its geometric properties. Also, we obtain several interesting results. Among others, the universal cover of this manifold splits geometrically as L(1)xN(n-1), where L is a line, (Nn-1, g(Nn-1)) is Einstein, phi = -1/n r . Moreover, we demonstrate the applications of the conformally symmetric generalized Ricci-recurrent spacetime with non-zero constant scalar curvature in the theory of general relativity.