Möbius invariant quaternion geometry

Porter, R.

doi:10.1090/S1088-4173-98-00032-0

Möbius invariant quaternion geometry
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by R. Michael Porter

Conform. Geom. Dyn. 2 (1998), 89-106

DOI: https://doi.org/10.1090/S1088-4173-98-00032-0

Published electronically: 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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