On characterizations of real hypersurface in complex space form with Codazzi type structure Lie operator

Abstract

In this paper, we prove that if \((\nabla _{X} L_{\xi })Y= (\nabla _{Y} L_{\xi })X\) holds on \(M\), then \(M\) is a Hopf hypersurface, where \(L_\xi \) denote the induced operator from the Lie derivative with respect to the structure vector field \(\xi \). We characterize such Hopf hypersurfaces of \(M_n(c)\).