Some Conditions Concerning the Shape Operator of a Real Hypersurface in Complex Projective Space

Let M be a real hypersurface of a complex projective space. For any operator B on M and any nonnull real number k, we can define two tensor fields of type (1,2) onM, B(k)F and B(k)T . We will classify real hypersurfaces in complex projective space for which B(k) F and B(k) T either take values in the maximal holomorphic distribution D or are parallel to the structure vector field ξ , in the particular case of B = A, where A denotes the shape operator of M. We also introduce the concept of A(k) F and A(k)Tbeing D-recurrent and classify real hypersurfaces such that either A(k) F or A(k) T are D-recurrent.