1204.6151 (Paul Tod)

Some examples of the behaviour of conformal geodesics    [PDF]

Paul Tod

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.

View original: http://arxiv.org/abs/1204.6151