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March 2015 Non-hyperbolic closed geodesics on Finsler spheres
Wei Wang
J. Differential Geom. 99(3): 473-496 (March 2015). DOI: 10.4310/jdg/1424880983

Abstract

In this paper, we prove that for every bumpy Finsler $2k$-sphere $(S^{2k}, F)$ with reversibility $\lambda$ and flag curvature $K$ satisfying the pinching condition $(\frac{\lambda}{\lambda + 1}) \lt K \leq 1$ either there exist infinitely many closed geodesics or there exist at least $2k$ non-hyperbolic closed geodesics. Due to the example of A. B. Katok, this estimate is sharp.

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Wei Wang. "Non-hyperbolic closed geodesics on Finsler spheres." J. Differential Geom. 99 (3) 473 - 496, March 2015. https://doi.org/10.4310/jdg/1424880983

Information

Published: March 2015
First available in Project Euclid: 25 February 2015

zbMATH: 1326.53110
MathSciNet: MR3316974
Digital Object Identifier: 10.4310/jdg/1424880983

Rights: Copyright © 2015 Lehigh University

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Vol.99 • No. 3 • March 2015
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