2024/12/06 by Boris Kruglikov, Kruglikov, Boris, Vladimir S. Matveev +3 · 1 citation
Mathematics · #Analytic and geometric function theory #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2412.04890
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.