Abstract
In this paper we show the existence of at least two distinct non-contractible closed geodesics on \({\mathbb {R}}P^3\) endowed with a bumpy and irreversible Finsler metric. If the bumpy metric F is reversible or Riemannian, there exist at least two geometrically distinct non-contractible closed geodesics on \({\mathbb {R}}P^{2n+1}\).
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Communicated by P. Rabinowotz.
H. Duan was Partially supported by NNSF (No. 11131004, 11471169), LPMC of MOE of China and Nankai University.
Y. Long was Partially supported by NSFC (No. 11131004), MCME and LPMC of MOE of China, Nankai University and BCMIIS of Capital Normal University.
Y. Xiao was Partially supported by the Funds for Young Teachers of Sichuan University.
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Duan, H., Long, Y. & Xiao, Y. Two closed geodesics on \({\mathbb {R}}P^{2n+1}\) with a bumpy Finsler metric. Calc. Var. 54, 2883–2894 (2015). https://doi.org/10.1007/s00526-015-0887-1
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DOI: https://doi.org/10.1007/s00526-015-0887-1