A characterization of ruled hypersurfaces in complex space forms in terms of the Lie derivative of shape operator

Abstract

In this paper, it is proved that if a non-Hopf real hypersurface in a nonflat complex space form of complex dimension two satisfies Ki and Suh's condition (J. Korean Math. Soc., 32 (1995), 161–170), then it is locally congruent to a ruled hypersurface or a strongly 2-Hopf hypersurface. This extends Ki and Suh's theorem to real hypersurfaces of dimension greater than or equal to three.

Keywords

• real hypersurface
• complex space form
• ruled hypersurface
• lie derivative