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On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity. (English) Zbl 1274.53049
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 is proved by an explicit example. Some geometric properties are 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 spacetimes. We obtain the Segre characteristic of such a spacetime.
Reviewer: Reviewer (Berlin)

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53B20 Local Riemannian geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B15 Other connections
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