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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Möbius invariant quaternion geometry
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by R. Michael Porter PDF
Conform. Geom. Dyn. 2 (1998), 89-106 Request permission

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.
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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
  • 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
  • © Copyright 1998 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 2 (1998), 89-106
  • MSC (1991): Primary 53A55; Secondary 53B10, 15A66, 51N30, 20G20
  • DOI: https://doi.org/10.1090/S1088-4173-98-00032-0
  • MathSciNet review: 1649091