Lagrangian decomposability of some two-generator subgroups of PU(2,1)

We describe isometry groups of the complex hyperbolic plane generated by two loxodromic motions. We give then a condition for such a group to be decomposable as a group generated by 3 antiholomorphic involutions, and use this decomposition to describe a 3-dimensional ball in the $\mathrm{PU}(2,1)$ Teichmüller space of the once punctured torus. To cite this article: P. Will, C. R. Acad. Sci. Paris, Ser. I 340 (2005).