A couple of real hyperbolic disc bundles over surfaces

Abstract

Applying the techniques developed in [1], we construct new real hyperbolic manifolds whose underlying topology is that of a disc bundle over a closed orientable surface. By the Gromov–Lawson–Thurston conjecture [6], such bundles M \to S should satisfy the inequality |eM/\chi S|\leq 1 , where eM stands for the Euler number of the bundle and \chi S , for the Euler characteristic of the surface. In this paper, we construct new examples that provide a maximal value of |eM/\chi S|=\frac {3}{5} among all known examples. The former maximum, belonging to Feng Luo [10], was |eM/\chi S|=\frac {1}{2} .