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Invariant Metrics for the Quaternionic Hardy Space

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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.

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Acknowledgments

Nicola Arcozzi partially supported by the PRIN project Real and Complex Manifolds of the Italian MIUR and by INDAM-GNAMPA. Giulia Sarfatti partially supported by INDAM-GNSAGA and by the PRIN project Real and Complex Manifolds of the Italian MIUR.

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  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 , Bologna, Italy

    Nicola Arcozzi & Giulia Sarfatti

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  1. Nicola Arcozzi
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  2. Giulia Sarfatti
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Correspondence to Nicola Arcozzi.

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Communicated by Alexander Isaev.

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Arcozzi, N., Sarfatti, G. Invariant Metrics for the Quaternionic Hardy Space. J Geom Anal 25, 2028–2059 (2015). https://doi.org/10.1007/s12220-014-9503-4

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  • DOI: https://doi.org/10.1007/s12220-014-9503-4

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