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

Uday Chand De, Avik De (2012)

Czechoslovak Mathematical Journal

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...

On F 2 ε -planar mappings of (pseudo-) Riemannian manifolds

Irena Hinterleitner, Josef Mikeš, Patrik Peška (2014)

Archivum Mathematicum

We study special F -planar mappings between two n -dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced P Q ε -projectivity of Riemannian metrics, ε 1 , 1 + n . Later these mappings were studied by Matveev and Rosemann. They found that for ε = 0 they are projective. We show that P Q ε -projective equivalence corresponds to a special case of F -planar mapping studied by Mikeš and Sinyukov (1983) and F 2 -planar mappings (Mikeš, 1994), with F = Q . Moreover, the tensor P is derived from the tensor Q and the non-zero...

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