On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces. (English) Zbl 1008.53020

Deszcz, Ryszard; Hotloś, Marian; Ṣentürk, Zerrin

Soochow J. Math. 27, No. 4, 375-389 (2001).

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 \(S=\alpha g+\beta w\otimes w\) where \(\alpha\) and \(\beta\) 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.

Reviewer: Eric Boeckx (Leuven)

MSC:

53B20	Local Riemannian geometry
53B25	Local submanifolds
53B30	Local differential geometry of Lorentz metrics, indefinite metrics
53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords:

pseudo-symmetry type manifolds; quasi-Einstein hypersurfaces