Note on non-discrete complex hyperbolic triangle groups of type $(n,n,\infty;k)$

Abstract

A complex hyperbolic triangle group is a group generated by three complex involutions fixing complex lines in complex hyperbolic space. In a previous paper~[3] we discussed complex hyperbolic triangle groups of type $(n,n,\infty;k)$ and proved that for $n \geq 29$ these groups are not discrete. In this paper we show that if $n \geq 22$, then complex hyperbolic triangle groups of type $(n,n,\infty;k)$ are not discrete and give a new list of non-discrete groups of type $(n,n,\infty;k)$.