Curvature properties of Cartan hypersurfaces
Ryszard Deszcz, Sahnur Yaprak (1994)
Colloquium Mathematicae
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Ryszard Deszcz, Sahnur Yaprak (1994)
Colloquium Mathematicae
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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.
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.
Johan Deprez, Piet A. Verheyen, Leopold C. A. Verstraelen (1985)
Czechoslovak Mathematical Journal
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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.
Defever, Filip (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Katarzyna Sawicz (2006)
Publications de l'Institut Mathématique
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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.
Kadri Arslan, Ryszard Deszcz, Şahnur Yaprak (1997)
Colloquium Mathematicae
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Małgorzata Głogowska (2005)
Banach Center Publications
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We investigate curvature properties of hypersurfaces in semi-Riemannian spaces of constant curvature with the minimal polynomial of the second fundamental tensor of second degree. We present suitable examples of hypersurfaces.