AI 中文总结
本文研究无共轭点且具常S-曲率的闭芬斯勒流形的刚性，证明满足特定条件的闭C^ω或C^∞芬斯勒流形必为黎曼流形，进而得到相关刚性结果，方法基于Cartan向量场与Green丛几何的分析。
AI 中文摘要
我们研究无共轭点的闭芬斯勒流形在S-曲率假设下的刚性现象。我们证明，具有常S-曲率、连续Green丛且包含一条双曲闭测地线的闭C^ω芬斯勒流形必为黎曼流形；在C^∞情形下，若额外满足测地流可传递的条件，该结论同样成立。由此，我们得到了具有一致可视万有覆盖的芬斯勒流形的刚性结果。我们的方法基于将Cartan向量场作为Jacobi场进行分析，及其与Green丛几何的相互作用。
英文摘要
We study rigidity phenomena in closed Finsler manifolds without conjugate points under assumptions on the $S$-curvature. We prove that a closed $C^ω$ Finsler manifold with constant $S$-curvature, continuous Green bundles, and admitting a hyperbolic closed geodesic must be Riemannian. In the $C^\infty$ setting, the same conclusion holds under the additional assumption that the geodesic flow is transitive. As a consequence, we obtain rigidity results for Finsler manifolds with uniform visibility universal covering. Our approach is based on the analysis of the Cartan vector field as a Jacobi field and its interaction with the geometry of Green bundles.
