Almost Ricci Solitons and Physical Applications

Year 2017, Volume: 10 Issue: 2, 1 - 10, 29.10.2017

Krishan Lal Duggal

Abstract

In this paper, we establish a link between a “curvature inheritance symmetry" of a semi-Riemannian

manifold and a class of almost Ricci solitons(ARS). In support of this link we present three

mathematical models of conformally flat ARS-manifolds. As an application to relativity, by

investigating the kinematic and dynamic properties of ARS-spacetimes we present a physical

model of three classes (namely, shrinking, steady and expanding) of perfect fluid solutions

for ARS-spacetimes and prove the existence of a family of totally umbilical ARS Einstein

hypersurfaces of a GRW-spacetime. Finally, we propose two open problems for further study.

Keywords

Ricci solitons, curvature symmetry, totally umbilical, Einstein spaces

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