论文标题
分支机构在亚riemannian几何形状中
Branching geodesics in sub-Riemannian geometry
论文作者
论文摘要
在本说明中，我们表明，亚riemannian歧管可以包含正常的分支最小化的大地测量学。这种现象发生在且仅当正常的大地测量在非零时间的等级中具有不连续性而发生，这尤其是对严格正常的地测量意味着它包含一个非平凡的异常子段。最简单的示例是通过以合适的方式将三维马丁内特扁平结构与海森堡组粘合在一起获得的。然后，我们使用此示例来构建更多一般类型的分支类型。
In this note, we show that sub-Riemannian manifolds can contain branching normal minimizing geodesics. This phenomenon occurs if and only if a normal geodesic has a discontinuity in its rank at a non-zero time, which in particular for a strictly normal geodesic means that it contains a non-trivial abnormal subsegment. The simplest example is obtained by gluing the three-dimensional Martinet flat structure with the Heisenberg group in a suitable way. We then use this example to construct more general types of branching.
