We define the Teichmüller pseudodistance on the space of spherical CR structures on a fixed compact manifold by using quasiconformal mappings between spherical CR manifolds.The pseudodistance is shown to be a complete distance.
This paper gets the Beltrami equations satisfied by a 1-quasiconformal map- ping, which are exactly CR or anti-CR equations on (2,2)-type quadric Q0. This means a 1-quasiconformal mapping on Q0 is CR or anti-CR. This reduces the determination of 1- quasiconformal mappings to a problem on the theory of several complex analysis. The result about the group of CR automorphisms is used to determine the unit component of group of 1-quasiconformal mappings.
