Conformal geodesics cannot spiral
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.
scientific article; zbMATH DE number 7939775