Integrable geodesic flows on the suspensions of toric automorphisms

Details Integrable geodesic flows on the suspensions of toric automorphisms Integrable geodesic flows on the suspensions of toric automorphisms

1999-11-24

arxiv.org/abs/math/9911193v2

Proceedings of the Steklov Institute of Math. 231 (2000), 42-58.

Mathematics

Differential Geometry

LaTeX, 23 pages, submitted to Proceedings of the Steklov Institute of Mathematics, some formulas and typos are corrected

Scientific paper

For any toric automorphism with only real eigenvalues a Riemannian metric with an integrable geodesic flow on the suspension of this automorphism is constructed. A qualitative analysis of such a flow on a three-solvmanifold constructed by the authors in math.DG/9905078 is done. This flow is an example of the geodesic flow, which has vanishing Liouville entropy and, moreover, is integrable but has positive topological entropy. The authors also discuss some open problems on integrability of geodesic flows and related subjects.

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