New conditions on some derivatives of the structure Lie operator on a real hypersurface in complex projective space

Abstract

Let $M$ be a real hypersurface in complex projective space equipped with both the Levi-Civita and $k$th generalized Tanaka-Webster connections, for any nonnull real number $k$. For any operator $B$ on $M$ we can define two tensor fields of type (1,2) on $M$, $B^{(k)}_F$ and $B^{(k)}_T$, related to both connections. In the particular case of $B = L$, the structure Lie operator on $M$, we study purity and hybridness of $L^{(k)}_F$ and $L^{(k)}_T$ with respect to the structure operator $\phi$.