Hyperbolic minimizing geodesics
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- by Daniel Offin PDF
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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.References
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Additional Information
- Daniel Offin
- Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
- Email: offind@mast.queensu.ca
- Received by editor(s): September 18, 1998
- Published electronically: March 21, 2000
- Additional Notes: This research supported in part by NSERC grant OGP0041872
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 3323-3338
- MSC (2000): Primary 37J45, 37J50, 58E30; Secondary 53C20, 34D08, 58E10
- DOI: https://doi.org/10.1090/S0002-9947-00-02483-1
- MathSciNet review: 1661274