Complex Hyperbolic Structures on Disc Bundles Over Surfaces

We study oriented disc bundles $M$ over a closed orientable surface $\Sigma$ that arise from certain discrete subgroups in $\PU(2,1)$ generated by reflections in ultraparallel complex lines in the complex hyperbolic plane $\Bbb H_{\Bbb C}^2$. The results obtained allow us to construct the first examples of$\bullet$ Disc bundles $M$ over $\Sigma$ that satisfy the equality $2(\chi+e)=3\tau$,$\bullet$ Disc bundles $M$ over $\Sigma$ that satisfy the inequality $\frac{1}{2}\chi