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On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity

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Abstract

The object of the present paper is to study almost pseudo-conformally symmetric Ricci-recurrent manifolds. The existence of almost pseudo-conformally symmetric Ricci-recurrent manifolds has been proved by an explicit example. Some geometric properties have been studied. Among others we prove that in such a manifold the vector field ϱ corresponding to the 1-form of recurrence is irrotational and the integral curves of the vector field ϱ are geodesic. We also study some global properties of such a manifold. Finally, we study almost pseudo-conformally symmetric Ricci-recurrent spacetime. We obtain the Segre’ characteristic of such a spacetime.

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Authors and Affiliations

  1. Department of Pure Mathematics, Calcutta University, 35-B. C. Road, Kolkata, 700019, India

    Uday Chand De & Avik De

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  1. Uday Chand De
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  2. Avik De
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Correspondence to Uday Chand De.

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Cordially dedicated to Professor W. Roter

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De, U.C., De, A. On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity. Czech Math J 62, 1055–1072 (2012). https://doi.org/10.1007/s10587-012-0063-0

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  • DOI: https://doi.org/10.1007/s10587-012-0063-0

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