Closed geodesics on positively curved Finsler spheres
نویسندگان
چکیده
منابع مشابه
Closed geodesics on positively curved Finsler spheres
In this paper, we prove that for every Finsler n-sphere (S, F ) for n ≥ 3 with reversibility λ and flag curvature K satisfying ( λ λ+1 )2 < K ≤ 1, either there exist infinitely many prime closed geodesics or there exists one elliptic closed geodesic whose linearized Poincaré map has at least one eigenvalue which is of the form exp(πiμ) with an irrational μ. Furthermore, there always exist three...
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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. 2000 MSC classification: 53C22; 53C60; 58E10
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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 indice...
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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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In this paper, we prove that on every Finsler n-sphere (S, F ) with reversibility λ satisfying F 2 < ( λ )g0 and l(S , F ) ≥ π(1 + 1 λ ), there always exist at least n prime closed geodesics without self-intersections, where g0 is the standard Riemannian metric on S n with constant curvature 1 and l(S, F ) is the length of a shortest geodesic loop on (S, F ). We also study the stability of thes...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2008
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.03.018