We consider a natural mechanical system on a Finsler manifold and study its curvature using the intrinsic Jacobi equations (called Jacobi curves) along the extremals of the least action of the system. The curvature for such a system is expressed in terms of the Riemann curvature and the Chern curvature (involving the gradient of the potential) of the Finsler manifold and the Hessian of the potential w.r.t. a Riemannian metric induced from the Finsler metric. As an application, we give sufficient conditions for the Hamiltonian flows of the least action to be hyperbolic and show new examples of Anosov flows.

中文翻译：

---

Finsler几何中自然机械系统的曲率和双曲流

我们考虑一个Finsler流形上的自然机械系统，并使用固有的Jacobi方程（称为Jacobi曲线）沿着系统作用最小的极值研究其曲率。这种系统的曲率用Finsler流形的Riemann曲率和Chern曲率（涉及电势的梯度）以及电势的Hessian（由Finsler度量导出的黎曼度量）表示。作为应用，我们为最小作用的哈密顿流给出了充分的条件是双曲线的，并给出了Anosov流的新示例。