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We study a CR analogue of the Ahlfors derivative for conformal immersions ofStowe [23] that generalizes the CR Schwarzian derivative studied earlier by thesecond-named author [21]. This notion possesses several important propertiessimilar to those of the conformal counterpart and provides a new invariant forspherically equivalent CR maps from strictly pseudoconvex CR manifolds into asphere. The invariant is computable and distinguishes many well-known spheremaps. In particular, it vanishes precisely when the map is sphericallyequivalent to the linear embedding of spheres.

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