Displaying similar documents to “On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms”

Quasi-Einstein hypersurfaces in semi-Riemannian space forms

Ryszard Deszcz, Marian Hotloś, Zerrin Sentürk (2001)

Colloquium Mathematicae

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We investigate curvature properties of hypersurfaces of a semi-Riemannian space form satisfying R·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.

On some class of hypersurfaces with three distinct principal curvatures

Katarzyna Sawicz (2005)

Banach Center Publications

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We investigate hypersurfaces M in spaces of constant curvature with some special minimal polynomial of the second fundamental tensor H of third degree. We present a curvature characterization of pseudosymmetry type for such hypersurfaces. We also prove that if such a hypersurface is a manifold with pseudosymmetric Weyl tensor then it must be pseudosymmetric.

On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez (2015)

Commentationes Mathematicae Universitatis Carolinae

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Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is...

Compact hypersurfaces with constant higher order mean curvatures.

Antonio Ros Mulero (1987)

Revista Matemática Iberoamericana

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A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature H, for some r = 1, ..., n.