Integral points and the hyperbolicity of the complement of hypersurfaces.
Min Ru (1993)
Journal für die reine und angewandte Mathematik
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Min Ru (1993)
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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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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Claire C. Chan (1997)
Journal für die reine und angewandte Mathematik
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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.
Jürgen Berndt (1989)
Journal für die reine und angewandte Mathematik
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J.W. Bruce (1981)
Mathematica Scandinavica
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Wolfgang M. Schmidt (1986)
Monatshefte für Mathematik
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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.
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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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).
Angelo Vistoli (1993)
Inventiones mathematicae
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John I.E. Urbas (1990)
Mathematische Zeitschrift
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