Invariant fibration of geodesic flows

Abstract

Let (Σ, g) be a compact $C^2$ finslerian 3-manifold. If the geodesic flow of g is completely integrable, and the singular set is a tamely-embedded polyhedron, then ${\pi }_1(\Sigma )$ is almost polycyclic. On the other hand, if Σ is a compact, irreducible 3-manifold and ${\pi }_1(\Sigma )$ is infinite polycyclic while ${\pi }_2(\Sigma )$ is trivial, then Σ admits an analytic riemannian metric whose geodesic flow is completely integrable and singular set is a real-analytic variety. Additional results in higher dimensions are proven.

28 pages. Published in 2005

Cited by in corpus (2)

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