Two closed geodesics on \({\mathbb {R}}P^{2n+1}\) with a bumpy Finsler metric

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• 作者：Huagui Duan ; Yiming Long ; Yuming Xiao
• 关键词：53C22 ; 58E05 ; 58E10
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：54
• 期：3
• 页码：2883-2894
• 全文大小：448 KB
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• 作者单位：Huagui Duan (1)
  Yiming Long (2)
  Yuming Xiao (3)
  
  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, People鈥檚 Republic of China
  2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, People鈥檚 Republic of China
  3. School of Mathematics, Sichuan University, Chengdu, 610064, People鈥檚 Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835

文摘

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 \({\mathbb {R}}P^{2n+1}\). Mathematics Subject Classification 53C22 58E05 58E10