Real hypersurfaces of non-flat complex space forms with two generalized conditions on the Jacobi structure operator

Abstract We aim to classify the real hypersurfaces M in a Kaehler complex space form Mn(c) satisfying the two conditions φl=lφ, $\varphi l=l\varphi ,$where l=R(⋅,ξ)ξ and φ $l=R(\cdot ,\xi )\xi \text{ and }\varphi $is the almost contact metric structure of M, and (∇ξl)X= $\left( {{\nabla }_{\xi }}l \right)X=$ω(X)ξ, where where ω(X) is a 1-form and X is a vector field on M. These two conditions imply that M is a Hopf hypersurface and ω = 0.