Real Hypersurfaces with $\xi$ -Parallel Ricci Tensor in a Complex Space Form
Commun. Korean Math. Soc. 1998 Vol. 13, No. 4, 825-838
Seong Soo Ahn, Seung-Gook Han, Nam-Gil Kim, Seong-Baek Lee
Dong Shin University, Chosun University, Chosun University, Chosun University
Abstract : We prove that if a real hypersurface with constant mean curvature of a complex space form satisfying $\nabla_{\xi}S=0$ and $S \xi = \sigma \xi$ for a smooth function $\sigma,$ then the structure vector field $\xi$ is principal, where $S$ denotes the Ricci tensor of the hypersurface.
Keywords : $\xi $-parallel Ricci tensor, principal curvature, real hypersurface, mean curvature
MSC numbers : 53C15, 53C45
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