RICCI OPERATORS AND STRUCTURAL JACOBI OPERATORS ON REAL HYPERSURFACES IN A COMPLEX SPACE FORM

Abstract

We give a classification of real hypersurfaces in a non-flat complex space form, whose almost contact structure operator, induced from the complex structure of the complex space form, commutes with the Ricci operator and at the same time commutes with the structural Jacobi operator. In particular, we classify real hypersurfaces in 2-dimensional complex projective and hyperbolic spaces satisfying the first commutativity condition.