Variationality of conformal geodesics in dimension 3

Autor:	Kruglikov, Boris, Matveev, Vladimir S., Steneker, Wijnand
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.04890 Zobrazit plný text záznamu View this record from Arxiv