The object of the present paper is to study a spacetime admitting conharmonic curvature tensor and some geometric properties related to this spacetime. It is shown that in a conharmonically flat spacetime with cyclic parallel Ricci tensor, the energy-momentum tensor is cyclic parallel and conversely. Finally, we prove that for a radiative perfect fluid spacetime if the energy-momentum tensor satisfying the Einstein's equations without cosmological constant is generalized recurrent, then the fluid has vanishing vorticity and the integral curves of the vector field U are geodesics. © 2017 World Scientific Publishing Company.

U C DE

S MALLICK

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

On a type of spacetime

International Journal of Geometric Methods in Modern Physics

The object of this paper is to study spacetimes admitting W 2-curvature tensor. At first we prove that a W2-flat spacetime is conformally flat and hence it is of Petrov type O. Next, we prove that if the perfect fluid spacetime with vanishing W2-curvature tensor obeys Einstein's field equation without cosmological constant, then the spacetime has vanishing acceleration vector and expansion scalar and the perfect fluid always behaves as a cosmological constant. It is also shown that in a perfect fluid spacetime of constant scalar curvature with divergence-free W 2-curvature tensor, the energy-momentum tensor is of Codazzi type and the possible local cosmological structure of such a spacetime is of type I, D or O. © 2014 World Scientific Publishing Company.

Spacetimes admitting W2-curvature tensor

It is shown that a general relativistic space-time with covariant-constant energy-momentum tensor is Ricci symmetric. Two particular types of such general relativistic space-times are considered and the nature of each is determined.

Journal	International Journal of Geometric Methods in Modern Physics
Publisher	World Scientific Publishing Co. Pte Ltd
ISSN	0219-8878