Shimizu’s Lemma for Quaternionic Hyperbolic Space

Cao, Wensheng; Parker, John R.

Abstract

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).

Citation

Cao, W., & Parker, J. R. (2018). Shimizu’s Lemma for Quaternionic Hyperbolic Space. Computational Methods and Function Theory - Springer, 18(1), 159-191. https://doi.org/10.1007/s40315-017-0212-4

• 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
• DOI: https://doi.org/10.1007/s40315-017-0212-4