On the average indices of closed geodesics on positively curved Finsler spheres |
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Authors: | Wei Wang |
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Affiliation: | 1. Beijing International Center for Mathematical Research, Key Laboratory of Pure and Applied Mathematics, School of Mathematical Science, Peking University, Beijing, 100871, People’s Republic of China
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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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