Minimal hypersurfaces in S4 with vanishing Gauss-Kronecker curvature.
Jayakumar Ramanathan (1990)
Mathematische Zeitschrift
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Displaying similar documents to “Complete minimal hypersurfaces in a locally symmetric space.”
Minimal hypersurfaces in S4 with vanishing Gauss-Kronecker curvature.
The geometry of closed hypersurfaces
Sebastião de Almeida, Fabiano Brito (1987-1988)
Séminaire de théorie spectrale et géométrie
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Minimal Hypersurfaces in the Space Form with Three Principal Curvatures.
Reiko Naka-Miyaoka (1980)
Mathematische Zeitschrift
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Minimal Hypersurfaces of S4 with Constant Gauss-Kronecker Curvature.
S.C. de Almeida, F.G. Braga Brito (1987)
Mathematische Zeitschrift
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Curvature conditions on hypersurfaces with two distinct principal curvatures
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.
On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds
Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez (2015)
Commentationes Mathematicae Universitatis Carolinae
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Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is...
A certain complete space-like hypersurface in Lorentz manifolds.
Kim, Hyang Sook, Kim, Young-Mi (2004)
Balkan Journal of Geometry and its Applications (BJGA)
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Characterization of totally umbilic hypersurfaces in a space form by circles
Toshiaki Adachi, Sadahiro Maeda (2005)
Czechoslovak Mathematical Journal
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In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.
Isoparametric hypersurfaces with less than four principal curvatures in a sphere
Toshiaki Adachi, Sadahiro Maeda (2006)
Colloquium Mathematicae
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We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.