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

Lamel, Bernhard; Son, Duong Ngoc

Annales de l'Institut Fourier, Tome 71 (2021) no. 5, pp. 2137-2167.

Nous étudions un analogue CR de la dérivée au sens d’Ahlfors pour les immersions conformes de Stowe, qui généralise la dérivée schwarzienne CR étudiée antérieurement par le second auteur. Cette notion possède plusieurs propriétés importantes similaires à celles de son homologue conforme et fournit un nouvel invariant pour les applications CR, sphériquement équivalentes, de variétés CR strictement pseudoconvexes à valeurs dans la sphère. Cet invariant est calculable et permet de distinguer beaucoup d’applications CR sphériques entre elles. En particulier, il s’annule précisément quand l’application est sphériquement équivalente au plongement linéaire entre sphères.

We study a CR analogue of the Ahlfors derivative for conformal immersions of Stowe that generalizes the CR Schwarzian derivative studied earlier by the second-named author. 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.

Classification : 32V05, 32H35, 53A30
Keywords: Sphere maps, Ahlfors derivative, CR maps
Mot clés : Applications sphériques, Dérivée d’Ahlfors, Applications CR

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