Hedgehogs of constant width and equichordal points
Yves Martinez-Maure (1997)
Annales Polonici Mathematici
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We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.
Yves Martinez-Maure (1997)
Annales Polonici Mathematici
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We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.
M. C. Lettington (2010)
Acta Arithmetica
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Kaising Tso (1989)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Kaising Tso (1992)
Mathematische Zeitschrift
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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.
Patrick J. Ryan (1972)
Colloquium Mathematicae
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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.
Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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F. Labourie (1987)
Inventiones mathematicae
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Wegner, Bernd (1990)
Portugaliae mathematica
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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).
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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Alan Weinstein, Christpher B. Croke (1981)
Inventiones mathematicae
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J.W. Bruce (1981)
Mathematica Scandinavica
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