Invariant metrics for the quaternionic Hardy space

Abstract

Riemannian metrics on the unit ball of the quaternions, which are naturally associated with the reproducing kernel Hilbert spaces. We study the metric arising from the Hardy space in detail. We show that, in contrast to the one-complex variable case, no Riemannian metric is invariant under regular self-maps of the quaternionic ball.

27 pages

References in corpus (2)

• Regular vs. classical Möbius transformations of the quaternionic unit ball
• Realizations of slice hyperholomorphic generalized contractive and positive functions