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

Author(s)
Duong Ngoc Son, Bernhard Lamel
Abstract

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.

Organisation(s)
Department of Mathematics
Journal
Annales de l'Institut Fourier
Volume
71
Pages
2137 - 2167
No. of pages
31
ISSN
0373-0956
Publication date
2021
Peer reviewed
Yes
Austrian Fields of Science 2012
101008 Complex analysis
Keywords
ASJC Scopus subject areas
Geometry and Topology, Algebra and Number Theory
Portal url
https://ucrisportal.univie.ac.at/en/publications/the-cr-ahlfors-derivative-and-a-new-invariant-for-spherically-equivalent-cr-maps(33ce69d0-ab04-469f-8d66-a4eb19142391).html