[Show abstract][Hide abstract] ABSTRACT: It is well-known that there exist no homogeneous ruled real hypersurfaces in a complex projective space. On the contrary there exists the unique homogeneous ruled real hypersurface in a complex hyperbolic space. Moreover, it is minimal. We characterize geometrically this minimal homogeneous real hypersurface by properties of extrinsic shapes of some curves.
Full-text · Article · Jan 2009 · Journal of the Mathematical Society of Japan
[Show abstract][Hide abstract] ABSTRACT: We characterize real hypersurfaces of type (A) and ruled real hypersurfaces in a complex projective space in terms of two φ-invariances of their shape operators, and give geometric meanings of these real hypersurfaces by observing their some geodesics.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we classify the real hypersurfaces in a non-flat complex space form with η-parallel shape operator.
KeywordsComplex space forms–Hopf hypersurfaces–Ruled real hypersurfaces–
η-parallel shape operator
No preview · Article · Oct 2011 · Mathematische Zeitschrift
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