Real hypersurfaces in complex hyperbolic two-plane Grassmannians related to the Reeb vector field

Abstract

In this paper we give a characterization of real hypersurfaces in noncompact complex two-plane Grassmannian $S{U}_{2,m}/S(U_2{U}_m)$, $m\ge 2$ with Reeb vector field $\xi$ belonging to the maximal quaternionic subbundle $\mathcal{Q}$. Then it becomes a tube over a totally real totally geodesic $\mathbb{H}{H}^n$, $m=2n$, in noncompact complex two-plane Grassmannian $S{U}_{2,m}/S(U_2{U}_m)$, a horosphere whose center at the infinity is singular or another exceptional case.

arXiv comment13pages