[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j170252

ON PSEUDO SEMI-PROJECTIVE SYMMETRIC MANIFOLDS

De, Uday Chand (Department of Pure Mathematics University of Calcutta)
Majhi, Pradip (Department of Pure Mathematics University of Calcutta)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 391-413 More about this Journal

Abstract

In this paper we introduce a new tensor named semi-projective curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds $(PSPS)_n$ which recover some known results of Chaki [5]. We provide several interesting results. Among others we prove that in a $(PSPS)_n$ if the associated vector field ${\rho}$ is a unit parallel vector field, then either the manifold reduces to a pseudosymmetric manifold or pseudo projective symmetric manifold. Moreover we deal with semi-projectively flat perfect fluid and dust fluid spacetimes respectively. As a consequence we obtain some important theorems. Next we consider the decomposability of $(PSPS)_n$ . Finally, we construct a non-trivial Lorentzian metric of $(PSPS)_4$ .

Keywords

semi-projective curvature tensor; $(PSPS)_n$ ; decomposable of $(PSPS)_n$ ; dust fluid; energy-momentum tensor; perfect fluid; Einstein's field equation; pseudo semi-projective symmetric manifolds;

Citations & Related Records

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