Regular vs. classical Möbius transformations of the quaternionic unit ball

Abstract

The regular fractional transformations of the extended quaternionic space have been recently introduced as variants of the classical linear fractional transformations. These variants have the advantage of being included in the class of slice regular functions, introduced by Gentili and Struppa in 2006, so that they can be studied with the useful tools available in this theory. We first consider their general properties, then focus on the regular Möbius transformations of the quaternionic unit ball B, comparing the latter with their classical analogs. In particular we study the relation between the regular Möbius transformations and the Poincaré metric of B, which is preserved by the classical Möbius transformations. Furthermore, we announce a result that is a quaternionic analog of the Schwarz-Pick lemma.

14 pages

References in corpus (6)

• Slice regular functions on real alternative algebras
• A new series expansion for slice regular functions
• Regular Moebius transformations of the space of quaternions
• Poles of regular quaternionic functions
• The Schwarz-Pick lemma for slice regular functions
• Möbius transformations and the Poincaré distance in the quaternionic setting

Cited by in corpus (7)

• Slice-quaternionic Hopf surfaces
• The harmonicity of slice regular functions
• A Landau's theorem in several complex variables
• Landau's theorem for slice regular functions on the quaternionic unit ball
• Some notions of subharmonicity over the quaternions
• Multipoint Schwarz-Pick Lemma for the quaternionic case
• Invariant metrics for the quaternionic Hardy space