Kisil, VV orcid.org/0000-0002-6593-6147 (2017) Poincaré extension of Möbius transformations. Complex Variables and Elliptic Equations, 62 (9). pp. 1221-1236. ISSN 1747-6933
Abstract
Given sphere preserving (Möbius) transformations in n-dimensional Euclidean space one can use the Poincaré extension to obtain sphere preserving transformations in a half-space of n+1 dimensions. The Poincaré extension is usually provided either by an explicit formula or by some geometric construction. We investigate its algebraic background and describe all available options. The solution is given in terms of one-parameter subgroups of Möbius transformations acting on triples of quadratic forms. To focus on the concepts, this paper deals with the Möbius transformations of the real line only.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Complex Variables and Elliptic Equations on 28 Dec 2016, available online: https://doi.org/10.1080/17476933.2016.1250399. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Möbius transformation, Poincaré extension, quadratic forms, Cayley–Klein geometries |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Dec 2015 12:38 |
Last Modified: | 28 Dec 2017 01:38 |
Published Version: | https://doi.org/10.1080/17476933.2016.1250399 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/17476933.2016.1250399 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92829 |