On semi-Riemannian manifolds satisfying some conformally invariant curvature condition
Volume 131 / 2013
Colloquium Mathematicum 131 (2013), 149-170
MSC: Primary 53B20, 53B25, 53B30, 53B50; Secondary 53C25, 53C40.
DOI: 10.4064/cm131-2-1
Abstract
We investigate semi-Riemannian manifolds with pseudosymmetric Weyl curvature tensor satisfying some additional condition imposed on their curvature tensor. Among other things we prove that the so-called Roter type equation holds on such manifolds. We present applications of our results to hypersurfaces in semi-Riemannian space forms, as well as to $4$-dimensional warped products.
