Conformal Geometry and Dynamics

Author(s): R. Michael Porter
Journal: Conform. Geom. Dyn. 2 (1998), 89-106.
MSC (1991): Primary 53A55; Secondary 53B10, 15A66, 51N30, 20G20
Posted: October 14, 1998
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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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Retrieve articles in Conformal Geometry and Dynamics with MSC (1991): 53A55, 53B10, 15A66, 51N30, 20G20

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: 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
Posted: October 14, 1998
Additional Notes: Partially supported by CONACyT grant 211085-5-2585P-E
Copyright of article: Copyright 1998, American Mathematical Society

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