The limit set of subgroups of a class of arithmetic groups

While lattices in semi-simple Lie groups are studied very well, only little is known about discrete subgroups of infinite covolume. The main class of examples are Schottky groups. Here we investigate some new examples.
We consider nonelementary subgroups of arithmetic groups in $PSL(2,C{)}^q\text{timesPSL}(2,R{)}^r$ with $q+r>1$ and their limit set. We give a necessary and sufficient condition for the projective limit set to be a point. Furthermore, we study the topology of the whole limit set.