Existence of closed geodesics on Finsler n-spheres

2009/09/19 by Wei Wang, Wang, Wei · 3 citations
Mathematics · #53C22 #53C60 #58E10 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C22 #msc:53C60 #msc:58E10

paper · pdf · doi:10.48550/arxiv.0909.3566

12 pages

arxiv created 2009/09/19 · arxiv updated 2009/12/01

Abstract

In this paper, we prove that on every Finsler n-sphere (Sⁿ, F) with reversibility λ satisfying F²<(\fracλ+1λ)²g₀ and l(Sⁿ, F)≥ π(1+\frac1λ), there always exist at least n prime closed geodesics without self-intersections, where g₀ is the standard Riemannian metric on Sⁿ with constant curvature 1 and l(Sⁿ, F) is the length of a shortest geodesic loop on (Sⁿ, F). We also study the stability of these closed geodesics.

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• Non-hyperbolic closed geodesics on positively curved Finsler spheres
• Two elliptic closed geodesics on positively curved Finsler spheres
• On the multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics

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