Closed Geodesics on Positively Curved Finsler 3-Spheres

Abstract

Abstract:In [33], Wang proved that for every Finsler three-dimensional sphere (S , F) with reversibility λ and flag curvature K satisfying (λ/( + λ)) < K ≤ , there exist at least three distinct closed geodesics. In this paper, we prove that for every Finsler three-dimensional sphere (S , F) with reversibility λ and flag curvature K satisfying ( / )(λ/( + λ)) < K ≤ with λ < , if there exist exactly three prime closed geodesics, then two of them are irrationally elliptic and the third one is infinitely degenerate.