LAUSR

Let M be a real hypersurface in a complex space form Mn(c), $${c \neq 0}$$c≠0. In this paper we prove that if $${R_{\xi}(\phi A - A\phi) + (\phi A - A\phi)R_{\xi} = 0}$$Rξ(ϕA-Aϕ)+(ϕA-Aϕ)Rξ=0 holds on M, then M is a Hopf hypersurface, where $${R_{\xi}}$$Rξ is the structure Jacobi operator, A is the shape operator of M in Mn(c) and $${\phi}$$ϕ is the tangential projection of the complex structure of Mn(c). We characterize such Hopf hypersurfaces of Mn(c).