Hypersurfaces of a Sasakian space form with recurrent shape operator

Abstract

Let $(M^{2n},g)$ be a real hypersurface with recurrent shape<br />operator and tangent to the structure vector field $xi$ of the Sasakian space form<br />$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ is<br />recurrent then it is parallel. Moreover, we show that $M$<br />is locally a product of two constant $phi-$sectional curvature<br />spaces.