Minimal Hypersurfaces in the Space Form with Three Principal Curvatures.
Reiko Naka-Miyaoka (1980)
Mathematische Zeitschrift
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Reiko Naka-Miyaoka (1980)
Mathematische Zeitschrift
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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.
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.
U. Abresch (1983)
Mathematische Annalen
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M.M. Kapranov (1991)
Mathematische Annalen
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Reiko Miyaoka (1982)
Mathematische Zeitschrift
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T. de Jong, D. van Straten (1990)
Mathematische Annalen
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John Harer (1978)
Mathematische Annalen
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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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U. Pinkall (1985)
Mathematische Annalen
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L. Simon, B. Solomon (1986)
Inventiones 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.
Claire C. Chan (1997)
Journal für die reine und angewandte Mathematik
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Bert Fischer (1996)
Mathematische Zeitschrift
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