Displaying similar documents to “On 2-quasi-umbilical pseudosymmetric hypersurfaces in the Euclidean space.”

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.

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 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.

A remark on almost umbilical hypersurfaces

Julien Roth (2013)

Archivum Mathematicum

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In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.