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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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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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.
Reiko Naka-Miyaoka (1980)
Mathematische Zeitschrift
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Qi-Ming Wang (1994)
Mathematische Annalen
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L. Simon, B. Solomon (1986)
Inventiones mathematicae
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Patrick J. Ryan (1972)
Colloquium Mathematicae
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Lin Jiu, Huafei Sun (2007)
Colloquium Mathematicae
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We give a classification of minimal homothetical hypersurfaces in an (n+1)-dimensional Euclidean space. In fact, when n ≥ 3, a minimal homothetical hypersurface is a hyperplane, a quadratic cone, a cylinder on a quadratic cone or a cylinder on a helicoid.
Reiko Miyaoka (1982)
Mathematische Zeitschrift
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Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Jürgen Berndt (1989)
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.
Leon Simon, Robert Hardt (1985)
Journal für die reine und angewandte Mathematik
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Klaus Steffen, Frank Duzaar (1994)
Journal für die reine und angewandte Mathematik
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Wolfgang M. Schmidt (1986)
Monatshefte für Mathematik
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