Quakebend deformations in complex hyperbolic quasi-Fuchsian space

We study quakebend deformations in complex hyperbolic quasi-Fuchsian space Q(C)(Sigma) of a closed surface Sigma of genus g > 1, that is the space of discrete, faithful, totally loxodromic and geometrically finite representations of the fundamental group of Sigma into the group of isometries of complex hyperbolic space. Emanating from an R-Fuchsian point rho epsilon Q(C)(Sigma), we construct curves associated to complex hyperbolic quakebending of rho and we prove that we may always find an open neighborhood U(rho) of rho in Q(C)(Sigma) containing pieces of such curves. Moreover, we present generalisations of the well known Wolpert-Kerckhoff formulae for the derivatives of geodesic length function in Teichmuller space.