On a conjecture of Anosov

2011/12/22 by Wei Wang, Wang, Wei · 3 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1112.5234

20 pages

arxiv created 2011/12/23 · arxiv updated 2011/12/26

Abstract

In this paper, we prove that for every bumpy Finsler n-sphere (Sⁿ, F) with reversibility λ and flag curvature K satisfying (\fracλλ+1)²<K≤ 1, there exist 2[(n+1)/(2)] prime closed geodesics. This gives a confirmed answer to a conjecture of D. V. Anosov \citeAno in 1974 for a generic case.

Cited by

• Multiple closed geodesics on positively curved Finsler manifolds
• Closed Reeb orbits on contact type hypersurfaces in T^*Sⁿ
• Non-hyperbolic closed geodesics on positively curved Finsler spheres

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