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October 2016 Two closed geodesics on compact simply connected bumpy Finsler manifolds
Huagui Duan, Yiming Long, Wei Wang
J. Differential Geom. 104(2): 275-289 (October 2016). DOI: 10.4310/jdg/1476367058

Abstract

We prove the existence of at least two distinct closed geodesics on a compact simply connected manifold $M$ with a bumpy and irreversible Finsler metric, when $H^* (M; \mathbf{Q}) \cong T_{d,h+1} (x)$ for some integer $h \geq 2$ and even integer $d \geq 2$. Consequently, together with earlier results on $S^n$, it implies the existence of at least two distinct closed geodesics on every compact simply connected manifold $M$ with a bumpy irreversible Finsler metric.

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Huagui Duan. Yiming Long. Wei Wang. "Two closed geodesics on compact simply connected bumpy Finsler manifolds." J. Differential Geom. 104 (2) 275 - 289, October 2016. https://doi.org/10.4310/jdg/1476367058

Information

Published: October 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1357.53086
MathSciNet: MR3557305
Digital Object Identifier: 10.4310/jdg/1476367058

Rights: Copyright © 2016 Lehigh University

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Vol.104 • No. 2 • October 2016
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