Quasi-Einstein hypersurfaces in semi-Riemannian space forms
Volume 89 / 2001
Colloquium Mathematicum 89 (2001), 81-97 MSC: 53B20, 53B30, 53B50, 53C25. DOI: 10.4064/cm89-1-6
We investigate curvature properties of hypersurfaces of a semi-Riemannian space form satisfying $R\cdot C=LQ(S,C)$, which is a curvature condition of pseudosymmetry type. We prove that under some additional assumptions the ambient space of such hypersurfaces must be semi-Euclidean and that they are quasi-Einstein Ricci-semisymmetric manifolds.