论文标题
表面上的路径几何链：理论和示例
Chains of path geometries on surfaces: theory and examples
论文作者
论文摘要
我们通过解决相关结构的等效问题来得出表面上路径几何形状的链方程：签名$（1,1）$的亚riemannian几何形状在触点3个manifold上。这种方法比解决路径几何形状的完整等效问题的标准方法要简单得多。然后，我们使用这些方程来从其链（投影到表面与路径一致的链中）进行投射路径几何形状的表征，并研究四个均匀路径几何示例的链。在这些示例之一（双曲平面中的肉眼）中，投影的链是双圆形四重奏。
We derive the equations of chains for path geometries on surfaces by solving the equivalence problem of a related structure: sub-Riemannian geometry of signature $(1,1)$ on a contact 3-manifold. This approach is significantly simpler than the standard method of solving the full equivalence problem for path geometry. We then use these equations to give a characterization of projective path geometries in terms of their chains (the chains projected to the surface coincide with the paths) and study the chains of four examples of homogeneous path geometries. In one of these examples (horocycles in the hyperbolic planes) the projected chains are bicircular quartics.
