Homogeneous spaces and isoparametric hypersurfaces.
Immervoll, Stefan (2008)
Beiträge zur Algebra und Geometrie
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Immervoll, Stefan (2008)
Beiträge zur Algebra und Geometrie
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Mehri Nasehi (2016)
Archivum Mathematicum
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In this paper we consider special examples of homogeneous spaces of arbitrary odd dimension which are given in [5] and [16]. We obtain the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces in both Riemannian and Lorentzian cases.
F. Labourie (1987)
Inventiones mathematicae
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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.
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).
Kim, Hyang Sook, Lee, Gil Sang, Pyo, Yong-Soo (1997)
Balkan Journal of Geometry and its Applications (BJGA)
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Krishan Duggal (2012)
Open Mathematics
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This paper deals with a family of lightlike (null) hypersurfaces (H u) of a Lorentzian manifold M such that each null normal vector ℓ of H u is not entirely in H u, but, is defined in some open subset of M around H u. Although the family (H u) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H u) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ...
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.
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 .
Floris Takens, Luchezar Stojanov (1993)
Mathematische Annalen
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