Some characterizations of real hypersurfaces of type (A) in a nonflat complex space form
Bull. Korean Math. Soc. 2007 Vol. 44, No. 1, 157-172
Printed March 1, 2007
U-Hang Ki and Huili Liu
The National Academy of Sciences, Northeastern University
Abstract : In this paper, we prove that if the structure Jacobi operator $R_{\xi}$ is $\xi$-parallel and $R_{\xi}$ commutes with the Ricci tensor $S$, then a real hypersurface with non-negative scalar curvature of a nonflat complex space form ${\rm M}_n(c)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in ${\rm M}_n(c)$.
Keywords : real hypersurface, structure Jacobi operator, Ricci tensor, Hopf hypersurface
MSC numbers : 53C40, 53C15
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