Displaying similar documents to “Quasi-Einstein hypersurfaces in semi-Riemannian space forms”

On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms

Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Leopold Verstraelen (2003)

Colloquium Mathematicae

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Solutions of the P. J. Ryan problem as well as investigations of curvature properties of Cartan hypersurfaces and Ricci-pseudosymmetric hypersurfaces lead to curvature identities holding on every hypersurface M isometrically immersed in a semi-Riemannian space form. These identities, under some assumptions, give rises to new generalized Einstein metric conditions on M. We investigate hypersurfaces satisfying such curvature conditions.

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...