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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Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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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.
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).
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.
Akivis, Maks A., Goldberg, Vladislav V. (1998)
Beiträge zur Algebra und Geometrie
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Andrew Baker, Nigel Ray (1982)
Mathematica Scandinavica
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J.W. Bruce (1981)
Mathematica Scandinavica
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Bert Fischer (1996)
Mathematische Zeitschrift
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Sadahiro Maeda, Toshiaki Adachi (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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We characterize curvature-adapted real hypersurfaces in nonflat quaternionic space forms in terms of their shape operators and structure tensors.
Angelo Vistoli (1993)
Inventiones mathematicae
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Reiko Miyaoka (1982)
Mathematische Zeitschrift
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Angelo Vistoli (1993)
Inventiones mathematicae
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Reiko Miyaoka (1984)
Mathematische Zeitschrift
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U. Abresch (1983)
Mathematische Annalen
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John I.E. Urbas (1990)
Mathematische Zeitschrift
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