Year: 2025
Type: article
Abstract: In this paper, we prove that, for every Finsler metric on S n S^{n} ( n ≥ 4 n\geq 4 ) with reversibility 𝜆 and flag curvature 𝐾 satisfying ( 2 n − 3 n − 1 ) 2 ( λ λ + 1 ) 2 < K ≤ 1 (\frac{2n-3}{n-1})^{2}(\frac{\lambda}{\lambda+1})^{2} and λ < n − 1 n − 2 \lambda<\frac{n-1}{n-2} , there exist at least 𝑛 prime closed geodesics on ( S n , F ) (S^{n},F) , which solves a conjecture of Katok and Anosov for such positively curved spheres when 𝑛 is even. Furthermore, if the number of closed geodesics on such positively curved Finsler S n S^{n} is finite, then there exist at least 2 [ n 2 ] − 1 2[\frac{n}{2}]-1 non-hyperbolic closed geodesics.
Authors: Huagui Duan, Dong Xie
Institution: Nankai University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416009285