The structure Jacobi operator on real hypersurfaces in a nonflat complex space form
Bull. Korean Math. Soc. 2005 Vol. 42, No. 2, 337-358 Printed June 1, 2005
U-Hang Ki, Soo Jin Kim, and Seong-Baek Lee Kyungpook National University, Chosun University, Chosun University
Abstract : Let $M$ be a real hypersurface with almost contact metric structure $(\phi, \xi, \eta, g)$ in a nonflat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_\xi$ commutes with both the structure tensor $\phi$ and the Ricc tensor $S$, then $M$ is a Hopf hypersurface in $M_n(c)$ provided that the mean curvature of $M$ is constant or $g(S\xi, \xi)$ is constant.
Keywords : structure Jacobi operator, Ricci tensor, Hopf hypersurface, nonflat complex space form