Open sets of maximal dimension in complex. hyperbolic quasi-Fuchsian space

Let pi(1), be the fundamental group of a closed surface Sigma of genus g > 1. One of the fundamental problems in complex hyperbolic geometry is to find all discrete, faithful, geometrically finite and purely loxodromic representations of pi(1) into SU(2, 1), (the triple cover of) the group of holomorphic isometries of H-C(2). In particular, given a discrete, faithful, geometrically finite and purely loxodromic representation rho(0) of pi(1), can we find an open neighbourhood of rho(0) comprising representations with these properties. We show that this is indeed the case when rho(0) preserves a totally real Lagrangian plane.