Conformal circles and parametrizations of curves in conformal manifolds
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- by T. N. Bailey and M. G. Eastwood PDF
- Proc. Amer. Math. Soc. 108 (1990), 215-221 Request permission
Abstract:
We give a simple ODE for the conformal circles on a conformal manifold, which gives the curves together with a family of preferred parametrizations. These parametrizations endow each conformal circle with a projective structure. The equation splits into two pieces, one of which gives the conformal circles independent of any parameterization, and another which can be applied to any curve to generate explicitly the projective structure which it inherits from the ambient conformal structure [1]. We discuss briefly the use of conformal circles to give preferred coordinates and metrics in the neighborhood of a point, and sketch the relationship with twistor theory in the case of dimension four.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 215-221
- MSC: Primary 53C22; Secondary 58G30, 83C60
- DOI: https://doi.org/10.1090/S0002-9939-1990-0994771-7
- MathSciNet review: 994771