On codimension-two subvarieties of hypersurfaces.
Ekaterina Amerik (1997)
Journal für die reine und angewandte Mathematik
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Ekaterina Amerik (1997)
Journal für die reine und angewandte Mathematik
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Jürgen Berndt (1991)
Journal für die reine und angewandte Mathematik
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Jürgen Berndt (1989)
Journal für die reine und angewandte Mathematik
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Patrick J. Ryan (1972)
Colloquium Mathematicae
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Claire C. Chan (1997)
Journal für die reine und angewandte Mathematik
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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.
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.
Wolfgang M. Schmidt (1986)
Monatshefte für Mathematik
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Kim, Hyang Sook, Pyo, Yong-Soo (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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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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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).
J.W. Bruce (1981)
Mathematica Scandinavica
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Angelo Vistoli (1993)
Inventiones mathematicae
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Klaus Steffen, Frank Duzaar (1994)
Journal für die reine und angewandte Mathematik
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