Real hypersufraces of non-flat complex hyperbolic planes whose Jacobi structure operator satisfies a generalized commutative condition

Abstract

Real hypersurfaces satisfying the condition $\phi l = l \phi$, $(l = R( . , \xi)\xi)$, have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex hyperbolic plane $\mathbb{C}H^{2}$ satisfying a generalization of $\phi l = l \phi$ under an additional restriction on a specific function.