Integrable geodesic flows on tubular sub-manifolds

19 Dec 2017  ·  Waters Thomas ·

In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dimensional manifolds, and using Jacobi fields we derive conditions under which the metric of the generalized tubular sub-manifold admits an ignorable coordinate... Some examples are given, demonstrating that these special surfaces can be quite elaborate and varied. read more

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Differential Geometry