The geometry of closed hypersurfaces
Sebastião de Almeida, Fabiano Brito (1987-1988)
Séminaire de théorie spectrale et géométrie
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Displaying similar documents to “Curvature conditions on hypersurfaces with two distinct principal curvatures”
The geometry of closed hypersurfaces
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Spacelike hypersurfaces with constant scalar curvature.
Qing-Ming Cheng, Susumu Ishikawa (1998)
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Characterizations of conformally flat hypersurfaces
Johan Deprez, Piet A. Verheyen, Leopold C. A. Verstraelen (1985)
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Hypersurfaces with constant inner curvature of the second fundamental form, and the non-rigidity of the sphere.
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Complete hypersurfaces with constant scalar curvature in a sphere
Ximin Liu, Hongxia Li (2005)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, by using Cheng-Yau’s self-adjoint operator , we study the complete hypersurfaces in a sphere with constant scalar curvature.
Minimal hypersurfaces in S4 with vanishing Gauss-Kronecker curvature.
Jayakumar Ramanathan (1990)
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On the quadric CMC spacelike hypersurfaces in Lorentzian space forms
Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos (2016)
Colloquium Mathematicae
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We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.
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.