Abstract
In this paper, we prove that on every Finsler n-sphere (S n, F) for n ≥ 6 with reversibility λ and flag curvature K satisfying \({(\frac{\lambda}{\lambda+1})^2 \, < \, K \, \le \, 1}\) , either there exist infinitely many prime closed geodesics or there exist \({[\frac{n}{2}]-2}\) closed geodesics possessing irrational average indices. If in addition the metric is bumpy, then there exist n−3 closed geodesics possessing irrational average indices provided the number of prime closed geodesics is finite.
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W. Wang was partially supported by National Natural Science Foundation of China No. 10801002, China Postdoctoral Science Foundation No. 200801021, Foundation for the Author of National Excellent Doctoral Dissertation of PR China No. 201017.
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Wang, W. On the average indices of closed geodesics on positively curved Finsler spheres. Math. Ann. 355, 1049–1065 (2013). https://doi.org/10.1007/s00208-012-0812-2
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DOI: https://doi.org/10.1007/s00208-012-0812-2