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

Abstract

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

21 pages, 1 table, final version accepted in Annales de l'institut Fourier

References in corpus (1)

• Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications

Cited by in corpus (2)

• On CR maps from the sphere into the tube over the future light cone
• On highly degenerate CR maps of spheres