Contact real hypersurfaces in the complex hyperbolic quadric

We give a new proof of the classification of contact real hypersurfaces with constant mean curvature in the complex hyperbolic quadric ${Q^m}^* = SO_{m,2}^o/SO_mSO_2$,where$m\geq 3$\mathrm{.}Weshowthatacontactrealhypersurface$M$in${Q^m}^$for$m\geq 3$islocallycongruenttoatubeofradius$r{\in}{\mathbb R}^+$aroundthecomplexhyperbolicquadric${Q^{m-1}}^$, or to a tube of radius $r\in {\mathbb{R}}^{+}$ around the $\mathfrak{A}$-principal $m$-dimensional real hyperbolic space $\mathbb{R}{H}^m$ in ${Q^m}^* = SO_{m,2}^o/SO_mSO_2$,ortoahorospherein${Q^{m-1}}^$inducedbyaclassof$\mathfrak A$-principalgeodesicsin${Q^m}^$.