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.
Citation
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
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