Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Gold Open Access
Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Möbius invariant quaternion geometry


Author: R. Michael Porter
Journal: Conform. Geom. Dyn. 2 (1998), 89-106
MSC (1991): Primary 53A55; Secondary 53B10, 15A66, 51N30, 20G20
Published electronically: October 14, 1998
MathSciNet review: 1649091
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A covariant derivative is defined on the one point compactification of the quaternions, respecting the natural action of quaternionic Möbius transformations. The self-parallel curves (analogues of geodesics) in this geometry are the loxodromes. Contrasts between quaternionic and complex Möbius geometries are noted.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (1991): 53A55, 53B10, 15A66, 51N30, 20G20

Retrieve articles in all journals with MSC (1991): 53A55, 53B10, 15A66, 51N30, 20G20


Additional Information

R. Michael Porter
Affiliation: Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del I.P.N., Apdo. Postal 14-740, 07000 México D. F., Mexico
Email: mike@math.cinvestav.mx

DOI: http://dx.doi.org/10.1090/S1088-4173-98-00032-0
PII: S 1088-4173(98)00032-0
Keywords: Quaternion, Möbius transformation, loxodrome, covariant derivative
Received by editor(s): January 29, 1998
Received by editor(s) in revised form: August 25, 1998
Published electronically: October 14, 1998
Additional Notes: Partially supported by CONACyT grant 211085-5-2585P-E
Article copyright: © Copyright 1998 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia