Real hypersurfaces in the complex hyperbolic quadric with Reeb parallel structure Jacobi operator

Abstract

We introduce the notion of Reeb parallel structure Jacobi operator for real hypersurfaces in the complex hyperbolic quadric ${Q^{\ast }}^m=S{O}_{2,m}^0/S{O}_{2}S{O}_m$, $m\ge 3$, and give a classification theory for real hypersurfaces in ${Q^{\ast }}^m$, $m\ge 3$, with Reeb parallel structure Jacobi operator.

23pages