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arXiv · 2104.13105

Variational principles for conformal geodesics

Maciej Dunajski·Wojciech Kryński
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Abstract

Conformal geodesics are solutions to a system of third order of equations, which makes a Lagrangian formulation problematic. We show how enlarging the class of allowed variations leads to a variational formulation for this system with a third--order conformally invariant Lagrangian. We also discuss the conformally invariant system of fourth order ODEs arising from this Lagrangian, and show that some of its integral curves are spirals.

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Maciej Dunajski, Wojciech Kryński. 2021-04-27. Variational principles for conformal geodesics. https://arxiv.org/abs/2104.13105

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