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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
