Abstract: Properties of Ricci-recurrent manifolds with some conditions imposed on the Weyl conformal curvature tensor are investigated. The main theorem states: a conformally quasi-recurrent and Ricci-recurrent but not Ricci-parallel manifold of dimension n>4 with nowhere vanishing Weyl conformal curvature tensor and Ricci tensor which is non-conformally related to a conformally symmetric one must be necessary Ricci-generalized pseudosymmetric manifold.
Keywords: Ricci-recurrent, Ricci-flat, conformally quasi-recurrent, conformally related, pseudosymmetry, Ricci-generalized pseudosymmetric.
Classification (MSC2000): 53B20
Full text of the article: