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.
- Jacobi field