REAL HYPERSURFACES SATISFYING ${\nabla}_{\xi}S$ = 0 OF A COMPLEX SPACE FORM

  • Kang, Eun-Hee (Topology and Geometry Research Center, Kyungpook National University) ;
  • Ki, U-Hang (Topology and Geometry Research Center, Kyungpook National University)
  • Published : 1998.11.01

Abstract

The main purpose of this paper is to prove that if a real hypersurfaces M of a complex space form satisfies ${\nabla}_{\xi}S$=0 and $S{\xi}=\sigma\xi$ for some constant on $\sigma$ on M, then the structure vector field $\xi$ is principal, where S denotes the Ricci tensors of M.