## Journal of Differential Geometry

### Two closed geodesics on compact simply connected bumpy Finsler manifolds

#### 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.

#### Article information

Source
J. Differential Geom., Volume 104, Number 2 (2016), 275-289.

Dates
First available in Project Euclid: 13 October 2016

https://projecteuclid.org/euclid.jdg/1476367058

Digital Object Identifier
doi:10.4310/jdg/1476367058

Mathematical Reviews number (MathSciNet)
MR3557305

Zentralblatt MATH identifier
1357.53086

#### Citation

Duan, Huagui; Long, Yiming; Wang, Wei. Two closed geodesics on compact simply connected bumpy Finsler manifolds. J. Differential Geom. 104 (2016), no. 2, 275--289. doi:10.4310/jdg/1476367058. https://projecteuclid.org/euclid.jdg/1476367058