Cyclic Parallel Structure Jacobi Operator for Real Hypersurfaces in the Complex Quadric

Abstract

First we give a classification of Hopf real hypersurfaces with $\eta$-parallel shape operator in the complex quadric $Q^{m}$, $m \geq 3$. As an application of this result, we give another classification of cyclic parallel structure Jacobi operator on Hopf real hypersurfaces in $Q^{m}$.