Hyperbolic minimizing geodesics

Offin, Daniel

doi:10.1090/S0002-9947-00-02483-1

Hyperbolic minimizing geodesics
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Trans. Amer. Math. Soc. 352 (2000), 3323-3338 Request permission

Abstract:

We apply the intersection theory for Lagrangian submanifolds to obtain a Sturm type comparison theorem for linearized Hamiltonian flows. Applications to the theory of geodesics are considered, including a sufficient condition that arclength minimizing closed geodesics, for an $n$-dimensional Riemannian manifold, are hyperbolic under the geodesic flow. This partially answers a conjecture of G. D. Birkhoff.

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