Characterizations of real hypersurfaces of type A in a complex space form

摘要

Let $M$ be a real hypersurface with almost contact metric structure $(phi, g, xi, eta)$ in a complex space form $M_n(c)$, $c eq 0$. In this paper we prove that if $R_xi mathcal L_xi g=0$ holds on $M$, then $M$ is a Hopf hypersurface in $M_n(c)$, where $R_xi$ and $mathcal L_x$ denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field $xi$ respectively. We characterize such Hopf hypersurfaces of $M_n(c)$.