Article
MSC:
53B15,
53B20,
53B30,
53C15,
53C25 | MR 3010256 | Zbl 1274.53049 | DOI: 10.1007/s10587-012-0063-0
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Keywords:
pseudo-conformally symmetric manifold; almost pseudo-conformally symmetric manifold; Ricci-recurrent manifold; Einstein field equations; Segre' characteristic
pseudo-conformally symmetric manifold; almost pseudo-conformally symmetric manifold; Ricci-recurrent manifold; Einstein field equations; Segre' characteristic
Summary:
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.
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