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Variationality of Conformal Geodesics in dimension 3
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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.
Springer Science and Business Media LLC
Title: Variationality of Conformal Geodesics in dimension 3
Description:
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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