2017/12/19 by Waters, Thomas
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1712.06896
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.