Variational principles for conformal geodesics
Differential Geometry
2021-09-22 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2104.13105,
title = {Variational principles for conformal geodesics},
author = {Maciej Dunajski and Wojciech Kryński},
journal= {arXiv preprint arXiv:2104.13105},
year = {2021}
}
Comments
14 pages, one figure. A gap removed from the proof of Corollary 4.2. Final version, to appear in Letters in Mathematical Physics