Displaying similar documents to “Semisymmetry and Ricci-symmetry for Hypersurfaces of Semi-euclidean Spaces”

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.

Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4 Пълна интегруемост на една нелинейна елиптична система, пораждаща би-омбилични фолирани полусиметрични хиперповърхнини в R^4

Kutev, Nikolai, Milousheva, Velichka (2010)

Union of Bulgarian Mathematicians

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Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4 We find explicitly all bi-umbilical foliated semi-symmetric hypersurfaces in the four- dimensional Euclidean space. *2000 Mathematics Subject Classification: 35A07, 35J60, 53A07, 53A10. The second author is partially supported by “L. Karavelov” Civil Engineering Higher School, Sofia, Bulgaria under Contract...

Parallel hypersurfaces

Barbara Opozda, Udo Simon (2014)

Annales Polonici Mathematici

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We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.

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.

Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces

Ryszard Deszcz, Malgorzata Głogowska (2002)

Colloquium Mathematicae

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We construct a class of nonsemisymmetric Ricci-semisymmetric warped products. Some manifolds of this class can be locally realized as hypersurfaces of a semi-Euclidean space s n + 1 , n ≥ 5.