  We prove a CR Obata type result that if the first positive eigenvalue of the
sub-Laplacian on a compact strictly pseudoconvex pseudohermitian manifold with
a divergence free pseudohermitian torsion takes the smallest possible value
then, up to a homothety of the pseudohermitian structure, the manifold is the
standart Sasakian unit sphere. We also give a version of this theorem using the
existence of a function with traceless horizontal Hessian on a complete, with
respect to Webster's metric, pseudohermitian manifold.
