Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324-2012

Article

Integrable geodesic flows on tubular sub-manifolds

DOI: 10.15673/tmgc.v10i3-4.770 (eng)


  • Томас Уотерс

Abstract | Full Text: 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.

Keywords:

  • geodesic
  • integrable
  • Jacobi field
  • tube