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Conformal Geometry and Dynamics

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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
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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.

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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

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

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