ON SEMI-RIEMANNIAN MANIFOLDS SATISFYING THE SECOND BIANCHI IDENTITY

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In this paper we introduce new notions of Ricci-like tensor and many kind of curvature-like tensors such that concir- cular, projective, or conformal curvature-like tensors defined on semi-Riemannian manifolds. Moreover, we give some geometric conditions which are equivalent to the Codazzi tensor, the Weyl tensor, or the second Bianchi identity concerned with such kind of curvature-like tensors respectively and also give a generalization of Weyl's Theorem given in (18) and (19).