Integrable geodesic flows on tubular sub-manifolds
Differential Geometry
2017-12-20 v1
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.
Cite
@article{arxiv.1712.06896,
title = {Integrable geodesic flows on tubular sub-manifolds},
author = {Thomas Waters},
journal= {arXiv preprint arXiv:1712.06896},
year = {2017}
}
Comments
Accepted Dec 2017 Proceedings of the International Geometry Center