论文标题
庞加莱 - 因斯坦和其他奇异的几何形状的杰出曲线和第一积分
Distinguished curves and first integrals on Poincaré-Einstein and other conformally singular geometries
论文作者
论文摘要
我们将定义和以实用方式定义和表征的问题，适当的一类庞加莱 - 因斯坦歧管的杰出曲线以及其他奇异的几何形状。这些“广义的大地测量学”与远离共形奇点集的大地测量学一致，并显示出在相遇或越过公制奇点集的点上满足自然的“边界条件”。我们还表征了它们与保形圆相吻合时。在（Poincaré-）爱因斯坦歧管的情况下，我们能够为这些杰出曲线提供非常通用的第一积分理论。除了概述的一般过程，还给出了一个具体示例。
We treat the problem of defining, and characterising in a practical way, an appropriate class of distinguished curves for Poincaré-Einstein manifolds, and other conformally singular geometries. These "generalised geodesics" agree with geodesics away from the conformal singularity set and are shown to satisfy natural "boundary conditions" at points where they meet or cross the metric singularity set. We also characterise when they coincide with conformal circles. In the case of (Poincaré-)Einstein manifolds, we are able to provide a very general theory of first integrals for these distinguished curves. As well as the general procedure outlined, a specific example is given.
