Czechoslovak Mathematical Journal, Vol. 62, No. 4, pp. 1055-1072, 2012

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

## Uday Chand De, Avik De

U. Chand De, A. De, Department of Pure Mathematics, Calcutta University, 35-B.C. Road, Kolkata-700019, India, e-mail: uc_de@yahoo.com

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 $\rho$ corresponding to the 1-form of recurrence is irrotational and the integral curves of the vector field $\rho$ 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.

Keywords: pseudo-conformally symmetric manifold, almost pseudo-conformally symmetric manifold, Ricci-recurrent manifold, Einstein field equations, Segre' characteristic

Classification (MSC 2010): 53C15, 53C25, 53B20, 53B30, 53B15

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