A class of complex hypersurfaces
Patrick J. Ryan (1972)
Colloquium Mathematicae
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Patrick J. Ryan (1972)
Colloquium Mathematicae
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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.
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.
Kim, Hyang Sook, Pyo, Yong-Soo (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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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).
Andrew Baker, Nigel Ray (1982)
Mathematica Scandinavica
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Akivis, Maks A., Goldberg, Vladislav V. (1998)
Beiträge zur Algebra und Geometrie
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J.W. Bruce (1981)
Mathematica Scandinavica
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Angelo Vistoli (1993)
Inventiones mathematicae
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Bert Fischer (1996)
Mathematische Zeitschrift
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Reiko Miyaoka (1982)
Mathematische Zeitschrift
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Angelo Vistoli (1993)
Inventiones mathematicae
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U. Abresch (1983)
Mathematische Annalen
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Reiko Miyaoka (1984)
Mathematische Zeitschrift
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John I.E. Urbas (1990)
Mathematische Zeitschrift
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Xu Mingwei (1992)
Mathematische Zeitschrift
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