The CR Ahlfors derivative and a new invariant for spherically equivalent CR maps

We study a CR analogue of the Ahlfors derivative for conformal immersions Stowe that generalizes Schwarzian studied earlier by second-named author. This notion possesses several important properties similar to those counterpart and provides new invariant spherically equivalent maps from strictly pseudoconvex manifolds into sphere. The is computable distinguishes many well-known sphere maps. In particular, it vanishes precisely when map linear embedding spheres.