Closed geodesics on positively curved spheres Sⁿ with Finsler metric induced by (ℝPⁿ,F)

2018/04/17 by Hui Liu, Wei Wang, Liu, Hui +1
Mathematics · Physics and Astronomy · #53C22 #53C60 #58E10 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1804.06193

openalex publication_date 2018/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It's well known that the n-sphere Sⁿ is the universal double covering of the n-dimensional real projective space ℝPⁿ and then any Finsler metric on ℝPⁿ induces a Finsler metric of Sⁿ. In this paper, we prove that for every Finsler (Sⁿ, F) for n≥3 whose metric is induced by irreversible Finsler (ℝPⁿ,F) with reversibility λ and flag curvature K satisfying (\fracλλ+1)²

Citations

• Multiple closed geodesics on positively curved Finsler manifolds

Related

• Closed geodesics on positively curved Finsler spheres
• On the minimal number of closed geodesics on positively curved Finsler spheres
• On the average indices of closed geodesics on positively curved Finsler spheres
• Existence of closed geodesics on Finsler n-spheres
• Existence of closed geodesics on positively curved Finsler manifolds