A new classifcation of contact hypersurfaces in the complex hyperbolic two-plane Grassmannian

Abstract

We give a complete classification of contact hypersurfaces in the complex hyperbolic two-plane Grassmannian $G_2^{\ast }\left({ℂ}^{m+2}\right)$, $m\ge 2$. In fact, they are locally congruent to a tube over a totally real totally geodesic $ℍH^n$, $m=2n$, in the complex hyperbolic two-plane Grassmannian $G_2^{\ast }\left({ℂ}^{m+2}\right)$, a horosphere whose center at the infinity is singular, or another exceptional case.