Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 19, No. 1, pp. 71-82 (2003)

On a class of Ricci-recurrent manifolds

Stanislaw Ewert-Krzemieniewski

Technical University of Szczecin, Poland

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

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