Integrable geodesic flows on tubular sub-manifolds

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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.
Original languageEnglish
Pages (from-to)17-28
Number of pages12
JournalProceedings of the International Geometry Center
Volume10
Issue number3-4
DOIs
Publication statusPublished - 20 Jan 2018

Keywords

  • geodesics
  • integrability
  • manifolds
  • Jacobi field
  • tube

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