Semi-parallel Lightlike Hypersurfaces of Indefinite Cosymplectic Space Forms
Abhitosh Upadhyay, Ram Shankar Gupta (2011)
Publications de l'Institut Mathématique
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Abhitosh Upadhyay, Ram Shankar Gupta (2011)
Publications de l'Institut Mathématique
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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.
Akivis, M.A., Goldberg, V.V. (1998)
Publications de l'Institut Mathématique. Nouvelle Série
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Mehri Nasehi (2016)
Czechoslovak Mathematical Journal
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In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally...
Gregory Galloway (1997)
Banach Center Publications
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Seon Mi Lyu, Juan de Dios Pérez, Young Jin Suh (2007)
Czechoslovak Mathematical Journal
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This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse image by the Hopf fibration of a real hypersurface in complex space form . In the second, we give a complete classification of real hypersurfaces in which satisfy the above geometric facts.
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.
U-Hang Ki, Makoto Kimura, Sadahiro Maeda (2001)
Czechoslovak Mathematical Journal
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We characterize homogeneous real hypersurfaces ’s of type , and of a complex projective space in the class of real hypersurfaces by studying the holomorphic distribution of .
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).
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.