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arXiv · 2412.04890

Variationality of conformal geodesics in dimension 3

Boris Kruglikov·Vladimir S. Matveev·Wijnand Steneker
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Abstract

Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The equation describing them is of third order, and it was an open problem whether they are given by an Euler--Lagrange equation. In dimension 3 (the simplest, but most important from the viewpoint of physical applications) we demonstrate that the equation for unparametrized conformal geodesics is variational.

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Boris Kruglikov, Vladimir S. Matveev, Wijnand Steneker. 2024-12-06. Variationality of conformal geodesics in dimension 3. https://doi.org/10.1007/s13324-025-01124-z

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