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Quasi-Einstein hypersurfaces in semi-Riemannian space forms. (English) Zbl 0991.53009
The paper is devoted to curvature properties of hypersurfaces of semi-Riemannian space forms satisfying some special condition of pseudosymmetry type. Under some special assumptions, the ambient manifold must be semi-Euclidean, and the respective hypersurfaces are quasi-Einstein Ricci-semisymmetric manifolds.
MSC:
53B30Lorentz metrics, indefinite metrics
53B20Local Riemannian geometry
53B50Applications of local differential geometry to physics
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)