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 Lorentzian Manifolds: A characterization with semiconformal curvature tensor Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 911-920 https://doi.org/10.4134/CKMS.c180248Published online July 31, 2019 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 Downloads: Full-text PDF   Full-text HTML