Characterizations of conformally flat hypersurfaces
Johan Deprez, Piet A. Verheyen, Leopold C. A. Verstraelen (1985)
Czechoslovak Mathematical Journal
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Johan Deprez, Piet A. Verheyen, Leopold C. A. Verstraelen (1985)
Czechoslovak Mathematical Journal
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de Dios Perez, Juan (1996)
International Journal of Mathematics and Mathematical Sciences
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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.
Hertrich-Jeromin, Udo (1994)
Beiträge zur Algebra und Geometrie
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Katarzyna Sawicz (2006)
Publications de l'Institut Mathématique
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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.
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.
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.
de Dios Pérez, Juan, Santos, Florentino G. (1991)
International Journal of Mathematics and Mathematical Sciences
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Katarzyna Sawicz (2004)
Colloquium Mathematicae
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We investigate hypersurfaces M in semi-Riemannian spaces of constant curvature satisfying some Ricci-type equations and for which the tensor H³ is a linear combination of the tensor H², the second fundamental tensor H of M and the metric tensor g of M.
Defever, Filip (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Dorić, M., Petrović-Torgašev, M., Verstraelen, L. (1988)
Publications de l'Institut Mathématique. Nouvelle Série
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