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Hyperbolic minimizing geodesics
Author(s):
Daniel
Offin
Journal:
Trans. Amer. Math. Soc.
352
(2000),
3323-3338.
MSC (2000):
Primary 37J45, 37J50, 58E30;
Secondary 53C20, 34D08, 58E10
Posted:
March 21, 2000
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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  -dimensional Riemannian manifold, are hyperbolic under the geodesic flow. This partially answers a conjecture of G. D. Birkhoff.
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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
DOI:
10.1090/S0002-9947-00-02483-1
PII:
S 0002-9947(00)02483-1
Received by editor(s):
September 18, 1998
Posted:
March 21, 2000
Additional Notes:
This research supported in part by NSERC grant OGP0041872
Copyright of article:
Copyright
2000,
American Mathematical Society
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