Geodesic
On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1055-1072.

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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.
DOI : 10.1007/s10587-012-0063-0
Classification : 53B15, 53B20, 53B30, 53C15, 53C25
Keywords: pseudo-conformally symmetric manifold; almost pseudo-conformally symmetric manifold; Ricci-recurrent manifold; Einstein field equations; Segre' characteristic 
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     title = {On almost pseudo-conformally symmetric {Ricci-recurrent} manifolds with applications to relativity},
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Chand De, Uday; De, Avik. On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1055-1072. doi : 10.1007/s10587-012-0063-0. http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0063-0/

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