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A characterization of totally η -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form

Mayuko Kon (2008)

Czechoslovak Mathematical Journal

We give a characterization of totally η -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator A of a real hypersurface M of a complex space form M n ( c ) , c 0 , n 3 , satisfies g ( A X , Y ) = a g ( X , Y ) for any X , Y T 0 ( x ) , a being a function, where T 0 is the holomorphic distribution on M , then M is a totally η -umbilical real hypersurface or locally congruent to a ruled real hypersurface....

A classification of certain submanifolds of an S-manifold

José L. Cabrerizo, Luis M. Fernández, Manuel Fernández (1991)

Annales Polonici Mathematici

A classification theorem is obtained for submanifolds with parallel second fundamental form of an 𝑆-manifold whose invariant f-sectional curvature is constant.

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