Isoparametric Hypersurfaces with Four or Six Distinct Principal Curvatures. Necessary Conditions on the Multiplicities.
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U. Abresch (1983)
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M.M. Kapranov (1991)
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T. de Jong, D. van Straten (1990)
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John Harer (1978)
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U. Pinkall (1985)
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Toshiaki Adachi, Sadahiro Maeda (2006)
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We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.
Patrick J. Ryan (1972)
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Ṣahin, Bayram, Güneṣ, Rifat (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Shanyu Ji (1993)
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F. Labourie (1987)
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James J.V. Faran (1977)
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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).
Reiko Miyaoka (1984)
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Sadahiro Maeda (1983)
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R.B. Melrose (1981)
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