Displaying similar documents to “Spacelike intersection curve of three spacelike hypersurfaces in E41”

Characterization of totally umbilic hypersurfaces in a space form by circles

Toshiaki Adachi, Sadahiro Maeda (2005)

Czechoslovak Mathematical Journal

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In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.

A Useful Characterization of Some Real Hypersurfaces in a Nonflat Complex Space Form

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).