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Shimizu’s Lemma for Quaternionic Hyperbolic Space

Cao, Wensheng; Parker, John R.

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Wensheng Cao


We give a generalisation of Shimizu’s lemma to complex or quaternionic hyperbolic space in any dimension for groups of isometries containing an arbitrary parabolic map. This completes a project begun by Kamiya (Hiroshima Math J 13:501–506, 1983). It generalises earlier work of Kamiya, Inkang Kim and Parker. The analogous result for real hyperbolic space is due to Waterman (Adv Math 101:87–113, 1993).


Cao, W., & Parker, J. R. (2018). Shimizu’s Lemma for Quaternionic Hyperbolic Space. Computational Methods and Function Theory - Springer, 18(1), 159-191.

Journal Article Type Article
Acceptance Date Jun 27, 2017
Online Publication Date Oct 23, 2017
Publication Date Mar 1, 2018
Deposit Date Sep 11, 2017
Publicly Available Date Sep 12, 2017
Journal Computational Methods and Function Theory - Springer
Print ISSN 1617-9447
Electronic ISSN 2195-3724
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 18
Issue 1
Pages 159-191


Accepted Journal Article (368 Kb)

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Copyright Statement
© The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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