Some examples of the behaviour of conformal geodesics
arXiv:1204.6151 · doi:10.1016/j.geomphys.2012.03.010
Abstract
With the aid of concrete examples, we consider the question of whether, in the presence of conformal curvature, a conformal geodesic can become trapped in smaller and smaller sets, or phrased informally: are spirals possible? We do not arrive at a definitive answer, but we are able to find situations where this behaviour is ruled out, including a reduction of the conformal-geodesic equations to quadratures in a specific non-conformally flat metric.
19 pages; to appear in Jour.Geom.Phys