To capture a multidimensional consistency feature of integrable systems in terms of geometry, we give a condition called geodesic compatibility implying the existence of integrals in involution of the geodesic flow. The geodesic compatibility condition is constructed from a concrete example namely the integrable Calogero's goldfish system through the Poisson structure and the variational principle. The geometrical view of the geodesic compatibility gives compatible parallel transports between two different Hamiltonian vector fields

中文翻译：

---

大地测量兼容性：金鱼系统

为了捕获可积系统在几何方面的多维一致性特征，我们给出了一个称为测地相容性的条件，这意味着测地流对合中存在积分。通过Poisson结构和变分原理，通过一个具体的例子，即可集成的Calogero金鱼系统，构造了测地线的相容性条件。大地测量兼容性的几何视图给出了两个不同哈密顿向量场之间的兼容并行传输