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arXiv · 1204.6151

Some examples of the behaviour of conformal geodesics

Paul Tod
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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.

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Paul Tod. 2012-04-27. Some examples of the behaviour of conformal geodesics. https://doi.org/10.1016/j.geomphys.2012.03.010

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