ON SEMI-RIEMANNIAN MANIFOLDS SATISFYING THE SECOND BIANCHI IDENTITY

Jung-Hwan Kwon, Yong-Soo Pyo, Young-Jin Suh
2003 Journal of the Korean Mathematical Society  
In this paper we introduce new notions of Ricci-like tensor and many kind of curvature-like tensors such that concircular, 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].
doi:10.4134/jkms.2003.40.1.129 fatcat:wor27qh6cvet5klhq7zthwznai