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.

arXiv comment21 pages, 1 table, final version accepted in Annales de l'institut Fourier

References in corpus (5)

• Homotopy equivalence for proper holomorphic mappings
• Flatness of CR Submanifolds in a Sphere
• The Schwarzian derivative and Möbius equation on strictly pseudo-convex CR manifolds
• The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces
• 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