On real hypersurfaces of type in a complex space form. III.
Kim, Hyang Sook, Pyo, Yong-Soo (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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Displaying similar documents to “Isoparametric Hypersurfaces in the Pseudo-Riemannian Space Forms.”
On real hypersurfaces of type in a complex space form. III.
Compact Dupin Hypersurfaces with Three Principal Curvatures.
Reiko Miyaoka (1984)
Mathematische Zeitschrift
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The hyperosculating spaces of hypersurfaces.
Xu Mingwei (1992)
Mathematische Zeitschrift
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Kernels of Martinelli-Bochner type on hypersurfaces.
Bert Fischer (1996)
Mathematische Zeitschrift
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Complete Hypersurfaces in the Space Form with Three Principal Curvatures.
Reiko Miyaoka (1982)
Mathematische Zeitschrift
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The Classification of Hypersurfaces of a Euclidean Space with Parallel Higher Order Fundamental Form.
F. Dillen (1990)
Mathematische Zeitschrift
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Non-existence of real lightlike hypersurfaces of an indefinite complex space form.
Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures.
John I.E. Urbas (1990)
Mathematische Zeitschrift
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A class of complex hypersurfaces
Patrick J. Ryan (1972)
Colloquium Mathematicae
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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.
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 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...
Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product
Eudes L. de Lima, Henrique F. de Lima, Eraldo A. Jr. Lima, Adriano A. Medeiros (2017)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.
On a Certain Class of Complex Einstein Hypersurfaces in Indefinite Complex Space Forms.
Alfonso Romero (1986)
Mathematische Zeitschrift
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Isoparametric Hypersurfaces with Four or Six Distinct Principal Curvatures. Necessary Conditions on the Multiplicities.
U. Abresch (1983)
Mathematische Annalen
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A Useful Characterization of Some Real Hypersurfaces in a Nonflat Complex Space Form
Takehiro Itoh, Sadahiro Maeda (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form M̃ₙ(c) (= ℂPⁿ(c) or ℂHⁿ(c)) and a real hypersurface of type (A₂) of radius π/(2√c) in ℂPⁿ(c) by observing the shape of some geodesics on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).