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 φ l = l φ , $\varphi l=l\varphi ,$ where l = R ( ⋅ , ξ ) ξ and φ $l=R(\cdot ,\xi )\xi \text{ and }\varphi $ is the almost contact metric structure of M, and ( ∇ ξ l ) 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.