Integrable geodesic flows on tubular sub-manifolds

Thomas Waters

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arXiv · 1712.06896

Integrable geodesic flows on tubular sub-manifolds

Thomas Waters

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Abstract

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.

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Thomas Waters. 2017-12-19. Integrable geodesic flows on tubular sub-manifolds. https://arxiv.org/abs/1712.06896

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