Addendum to the paper "Hypersurfaces with Isometric Reeb Flow in Complex hyperbolic Two-Plane Grassmannians"

Hyunjin Lee; Mi Jung Kim; Young Jin Suh

paper

Addendum to the paper "Hypersurfaces with Isometric Reeb Flow in Complex hyperbolic Two-Plane Grassmannians"

arXiv:1410.5934

Abstract

We classify all of real hypersurfaces $M$ with Reeb invariant shape operator in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S (U_{2} \cdot U_{m})$ , $m \geq 2$ . Then it becomes a tube over a totally geodesic $S U_{2, m - 1} / S (U_{2} \cdot U_{m - 1})$ in $S U_{2, m} / S (U_{2} \cdot U_{m})$ or a horosphere whose center at infinity is singular and of type $J N \in J N$ for a unit normal vector field $N$ of $M$ .