We find Riemannian metrics on the unit ball of the quaternions, which are naturally associated with 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 all regular self-maps of the quaternionic ball.
Arcozzi, N. (2015). Invariant metrics for the quaternionic Hardy space. THE JOURNAL OF GEOMETRIC ANALYSIS, 25(3), 2028-2059 [10.1007/s12220-014-9503-4].
Invariant metrics for the quaternionic Hardy space
ARCOZZI, NICOLA
2015
Abstract
We find Riemannian metrics on the unit ball of the quaternions, which are naturally associated with 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 all regular self-maps of the quaternionic ball.File in questo prodotto:
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