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Static perfect fluid spacetime with half conformally flat spatial factor

Article

Abstract

The aim of this paper is to investigate the static perfect fluid spacetime \(M^{4}\times _{f}\mathbb {R}\) such that \((M^4, g)\) is a half conformally flat Riemannian manifold. We prove that \((M^4, g)\) is, in fact, locally isometric to a warped product manifold \(I\times _{\phi }N^{3}\) where \(I\subset \mathbb {R}\) and \(N^{3}\) is a space form. Consequently, we make an analysis of the Fischer-Marsden conjecture for a 4-dimensional Riemannian manifold.

Mathematics Subject Classification

53C21 83C05 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universidade de Federal de JataíJataíBrazil
  2. 2.Universidade Federal da Integração Latino-AmericanaFoz do IguaçuBrazil

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