Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2019; 34(3): 911-920

Online first article July 8, 2019      Printed July 31, 2019

https://doi.org/10.4134/CKMS.c180248

Copyright © The Korean Mathematical Society.

Lorentzian Manifolds: A characterization with semiconformal curvature tensor

Uday Chand De, Chiranjib Dey

35, Ballygaunge Circular Road; Vill-Dhamla, P.O.-Kedarpur

Abstract

In this paper we characterize semiconformally flat spacetimes and a spacetime with harmonic semiconformal curvature tensor. At first in a semiconformally flat perfect fluid spacetime we obtain a state equation and prove that in particular for dimension $n=4$, the spacetime represents a model for incoherent radiation. Next we prove that perfect fluid spacetime with harmonic semiconformal curvature tensor is of Petrov type $I$, $D$ or $O$ and the spacetime is a GRW spacetime. As a consequence we obtain several corollaries.

Keywords: Lorentzian manifolds, conformal curvature tensor, semiconformal curvature tensor

MSC numbers: 53B30, 53C25, 53C50, 53C80