The object of the present paper is to introduce a non-flat Riemannian manifold called hyper-generalized recurrent manifolds and study its various geometric properties along with the existence of a proper example.
In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.
We study special -planar mappings between two -dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced -projectivity of Riemannian metrics, . Later these mappings were studied by Matveev and Rosemann. They found that for they are projective. We show that -projective equivalence corresponds to a special case of -planar mapping studied by Mikeš and Sinyukov (1983) and -planar mappings (Mikeš, 1994), with . Moreover, the tensor is derived from the tensor and the non-zero...
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.
In this paper we present a review of recent results on semi-Riemannian manifolds satisfying curvature conditions of pseudosymmetry type.