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Zbl 1008.53020
Deszcz, Ryszard; Hotloś, Marian; Ṣentürk, Zerrin
On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces.
(English)
[J] Soochow J. Math. 27, No.4, 375-389 (2001). ISSN 0250-3255

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.
[Eric Boeckx (Leuven)]
MSC 2000:
*53B20 Local Riemannian geometry
53B25 Local submanifolds
53B30 Lorentz metrics, indefinite metrics
53C25 Special Riemannian manifolds

Keywords: pseudo-symmetry type manifolds; quasi-Einstein hypersurfaces

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