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

Takehiro ItohSadahiro 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).

A characterization of a certain real hypersurface of type ( A 2 ) in a complex projective space

Byung Hak KimIn-Bae KimSadahiro Maeda — 2017

Czechoslovak Mathematical Journal

In the class of real hypersurfaces M 2 n - 1 isometrically immersed into a nonflat complex space form M ˜ n ( c ) of constant holomorphic sectional curvature c ( 0 ) which is either a complex projective space P n ( c ) or a complex hyperbolic space H n ( c ) according as c > 0 or c < 0 , there are two typical examples. One is the class of all real hypersurfaces of type (A) and the other is the class of all ruled real hypersurfaces. Note that the former example are Hopf manifolds and the latter are non-Hopf manifolds. In this...

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