Real hypersurfaces with Reeb invariant structure Jacobi operator in the complex quadric

Abstract

We introduce a new notion of Reeb invariant structure Jacobi operator and two kinds of singular normal vector field $N$ for a real hypersurface~$M$ in the complex quadric $Q^{m}$, $m \geq 3$. According to the $\mathfrak A$-isotropic unit normal $N$, we give a classification of Hopf real hypersurfaces with Reeb invariant structure Jacobi operator in the complex quadric $Q^{m}$ for $m \geq 3$.