New results on derivatives of the shape operator of a real hypersurface in a complex projective space

Abstract

We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka-Webster connections. For any nonnull real number k and any symmetric tensor field of type (1,1) L on M we can define a tensor field of type (1,2) on M, L(k) F , related to both connections. We study symmetry and skewsymmetry of the tensor A(k) F associated to the shape operatorA of M.