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On the equivalence of Ricci-semisymmetry and semisymmetry

1998
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Colloquium Mathematicum
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Introduction. A semi-Riemannian manifold (M, g), n = dim M ≥ 3, is said to be semisymmetric [28] if (1) R · R = 0 holds on M . It is well known that the class of semisymmetric manifolds includes the set of locally symmetric manifolds (∇R = 0) as a proper subset. Recently the theory of Riemannian semisymmetric manifolds has been presented in the monograph [1]. It is clear that every semisymmetric manifold satisfies The semi-Riemannian manifold (M, g), n ≥ 3, satisfying (2) is called

doi:10.4064/cm-76-2-279-294
fatcat:q5tu2p6crbeaxfc24j56rllwzq