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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

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).

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