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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hyperbolic minimizing geodesics


Author: Daniel Offin
Journal: Trans. Amer. Math. Soc. 352 (2000), 3323-3338
MSC (2000): Primary 37J45, 37J50, 58E30; Secondary 53C20, 34D08, 58E10
Published electronically: March 21, 2000
MathSciNet review: 1661274
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Daniel Offin
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Email: offind@mast.queensu.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02483-1
PII: S 0002-9947(00)02483-1
Received by editor(s): September 18, 1998
Published electronically: March 21, 2000
Additional Notes: This research supported in part by NSERC grant OGP0041872
Article copyright: © Copyright 2000 American Mathematical Society