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

Abstract

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) on M, BF(k) and BT(k) . We will classify real hypersurfaces in complex projective space for which BF(k) and BT(k) 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 AF(k) and AT(k) being D -recurrent and classify real hypersurfaces such that either AF(k) or AT(k) are D -recurrent.