Conformal geodesics cannot spiral
type: Item
instance of: scholarly article
title: Conformal geodesics cannot spiral
author: Peter Cameron
author: Maciej Dunajski
author: Paul Tod
published in: Journal of Differential Geometry
publication date: 2024-11-06T00:00:00Z
review text: A pseudo-Riemannian manifold \((M, g)\) defines a distinguished set of curves which are metric geodesics of \(g\). However, with the exception of null geodesics in the Lorentzian case, there is in general no relation between the metric geodesics of two conformally related metrics. Conformal geodesics can be thought of as a distinguished set of curves defined on a conformal manifold \((M, [g])\). These curves are solutions to a system of conformally invariant 3rd order ODEs and are uniquely specified locally by an initial position, unit tangent direction and perpendicular acceleration. In this paper the authors prove a general no-spiralling theorem for conformal geodesics.
reviewed by: Andrea Tamburelli
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C18
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 7939775
zbMATH Keywords: pseudo-Riemannian manifolds
zbMATH Keywords: conformal metrics
zbMATH Keywords: geodesics
MaRDI profile type: Publication
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DOI: 10.4310/JDG/1727712889
description: scientific article; zbMATH DE number 7939775