On curvature collineations on simple conformally recurrent manifolds
On the existence of certain types of Riemannian metrics
On a Certain Extension of the Class of Semisymmetric Manifolds
On the equivalence of the Ricci-pseudosymmetry and pseudosymmetry
Quasi-Einstein hypersurfaces in semi-Riemannian space forms
We investigate curvature properties of hypersurfaces of a semi-Riemannian space form satisfying R·C = LQ(S,C), which is a curvature condition of pseudosymmetry type. We prove that under some additional assumptions the ambient space of such hypersurfaces must be semi-Euclidean and that they are quasi-Einstein Ricci-semisymmetric manifolds.
On semi-Riemannian manifolds satisfying some conformally invariant curvature condition
We investigate semi-Riemannian manifolds with pseudosymmetric Weyl curvature tensor satisfying some additional condition imposed on their curvature tensor. Among other things we prove that the so-called Roter type equation holds on such manifolds. We present applications of our results to hypersurfaces in semi-Riemannian space forms, as well as to 4-dimensional warped products.
On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms
Solutions of the P. J. Ryan problem as well as investigations of curvature properties of Cartan hypersurfaces and Ricci-pseudosymmetric hypersurfaces lead to curvature identities holding on every hypersurface M isometrically immersed in a semi-Riemannian space form. These identities, under some assumptions, give rises to new generalized Einstein metric conditions on M. We investigate hypersurfaces satisfying such curvature conditions.
On some type of curvature conditions
In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.
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