Real hypersurfaces in CP² and CH² whose structure Jacobi operator is Lie D-parallel

Abstract

In [3], [7] and [8] results concerning the parallelness of the Lie derivative of the structure Jacobi operator of a real hypersurface with respect to and to any vector field X were obtained in both complex projective space and complex hyperbolic space. In the present paper, we study the parallelness of the Lie derivative of the structure Jacobi operator of a real hypersurface with respect to vector field X ∈ D in CP2 and CH2. More precisely, we prove that such real hypersurfaces do not exist.