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Elliptic closed geodesics on non-negatively curved Finsler manifolds
Abstract
In this paper, we prove that if a compact simply-connected manifold (M,F) with a bumpy irreversible Finsler metric F whose flag curvature K satisfies K≥ 0 and H*(M;Q)≅ Td,n+1(x) for some d∈2N and n∈N carries exactly (dn(n+1))/2 (the number of closed geodesics in Katok's example) closed geodesics, then there are at least $2$ irrationally elliptic closed geodesics on $(M, F)$.
Related
- Multiplicity of closed geodesics on odd-dimensional bumpy Finsler compact space form
- The second closed geodesic on Finsler manifolds with ℤ2 fundamental group
- Closed geodesics on compact semi-Riemannian manifolds
- Growth of Simple Closed Geodesics in Finite-Volume Hyperbolic Manifolds
- Simple geodesics in closed hyperbolic manifolds
BibTeX
@misc{wang2026elliptic,
title = {{Elliptic closed geodesics on non-negatively curved Finsler manifolds}},
author = {Wei Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25579},
eprint = {2610.25579},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25579},
}
RIS
TY - UNPB
TI - Elliptic closed geodesics on non-negatively curved Finsler manifolds
AU - Wei Wang
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25579
UR - https://arxiv.org/abs/2610.25579
AB - In this paper, we prove that if a compact simply-connected manifold (M,F) with a bumpy irreversible Finsler metric F whose flag curvature K satisfies K≥ 0 and H^*(M;Q)≅ T_d,n+1(x) for some d∈2N and n∈N carries exactly (dn(n+1))/2 (the number of closed geodesics in Katok's example) closed geodesics, then there are at least $2$ irrationally elliptic closed geodesics on $(M, F)$.
ER -