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On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces. (English) Zbl 1008.53020
This paper is part of an ongoing research programme of the authors and their collaborators concerning curvature properties of pseudo-symmetry type. Here they consider hypersurfaces M in semi-Euclidean spaces which are quasi-Einstein, i.e., their Ricci tensor S is of the form S=αg+βww where α and β are real numbers, g is the metric tensor and w a one-form on M. In particular, the interplay between properties of the shape operator of such hypersurfaces and curvature properties is studied.
MSC:
53B20Local Riemannian geometry
53B25Local submanifolds
53B30Lorentz metrics, indefinite metrics
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)