论文标题
里曼尼式飞机的有界距离地球叶
Bounded distance geodesic foliations in Riemannian planes
论文作者
论文摘要
猜想的烧伤和kniper虫问一个带有无共轭点的度量标准的2平面，以及带有线条的地球叶子的线条，其线处于有限的Hausdorff距离上，一定是平坦的。我们在两种情况下证明了这一猜想：在以下假设下：平面允许总曲率，并且在某个时候可见性的假设下。在此过程中，我们表明，Riemannian 2平面上的所有测量线叶子都必须同型标准。
A conjecture of Burns and Knieper asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this conjecture in two cases: under the hypothesis that the plane admits total curvature, and under the hypothesis of visibility at some point. Along the way, we show that all geodesic line foliations on a Riemannian 2-plane must be homeomorphic to the standard one.
