论文标题
图2-孔子上的八个大地测量学
Figure Eight Geodesics on 2-Orbifolds
论文作者
论文摘要
众所周知，在可定向双曲线的2孔菲尔德通过Orbifold的Orbifold点上，最短的非简单闭合地球封闭。这就提出了有关最小长度非简单闭合地球学与Orbifold点的疑问。在这里，我们探索了一旦自我切断的封闭的大地测量学与Orbifold的Orbifold点不相交，称为图八个大地测量学。使用基本域和基本双曲线三角学，我们识别和分类所有三角形组上的八个大地测量学。这种分类使我们能够在三角形组上找到最短的八个测量线，即（3,3,4） - 三角形群中的独特之处。然后，我们表明，同一曲线是双曲线的2-纤维上的最短八个曲线，没有阶次的阶点。
It is known that the shortest non-simple closed geodesic on an orientable hyperbolic 2-orbifold passes through an orbifold point of the orbifold. This raises questions about minimal length non-simple closed geodesics disjoint from the orbifold points. Here we explore once self-intersecting closed geodesics disjoint from the orbifold points of the orbifold, called figure eight geodesics. Using fundamental domains and basic hyperbolic trigonometry we identify and classify all figure eight geodesics on triangle group orbifolds. This classification allows us to find the shortest figure eight geodesic on a triangle group orbifold, namely the unique one on the (3,3,4)-triangle group orbifold. We then show that this same curve is the shortest figure eight geodesic on a hyperbolic 2-orbifold without orbifold points of order two.
