Lie derivatives and structure Jacobi operator on real hypersurfaces in complex projective spaces II

Abstract

Let M be a real hypersurface in complex projective space. The almost contact metric structure on M allows us to consider, for any nonnull real number k, the corresponding k-th generalized Tanaka-Webster connection on M and, associated to it, a differential operator of first order of Lie type. Considering such a differential operator and Lie derivative we define, from the structure Jacobi operator Rξ on M a tensor field of type (1,2), RξT(k). We obtain some classifications of real hypersurfaces for which RξT(k) is either symmetric or skew symmetric.