On the average indices of closed geodesics on positively curved Finsler spheres
نویسنده
چکیده
In this paper, we prove that on every Finsler n-sphere (S, F ) for n ≥ 6 with reversibility λ and flag curvature K satisfying ( λ λ+1 )2 < K ≤ 1, either there exist infinitely many prime closed geodesics or there exist [ 2 ] − 2 closed geodesics possessing irrational average indices. If in addition the metric is bumpy, then there exist n − 3 closed geodesics possessing irrational average indices provided the number of closed geodesics is finite.
منابع مشابه
Existence of closed geodesics on positively curved Finsler manifolds Hans - Bert Rademacher
For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.
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