Commutativity of the $h$-operator and two other operators on a real hypersurface in complex projective space

Abstract

The almost contact metric structure on a real hypersurface $M$ in complex projective space allows to define on $M$, for any nonnull real number $k$ and any operator $B$, two tensor fields of type (1,2) denoted by $B^{(k)}_F$ and $B^{(k)}_T$ .We will classify real hypersurfaces in complex projective space for which the $h$-operator satisfies that either $h^{(k)}_F = 0$ or $h^{(k)}_T = 0$.