论文标题
四面体上的简单封闭的准化学学
Simple Closed Quasigeodesics on Tetrahedra
论文作者
论文摘要
Pogorelov在1949年证明，每个凸多面体至少都有三个简单的封闭式准化学。尽管大地测量在每个点处的两侧都完全具有PI表面角度，而quasigeodesic最多在每个点的PI表面角度与两侧的两侧具有。 Pogorelov的存在证明并没有提出一种识别这三种Quasigeodesics的方法，直到最近才提出了有限的算法。 在这里，我们在任何四面体上识别出三个简单的封闭的准化学学：至少一个至1个顶点，至少一个至2个顶点，以及至少一个至少一个至3个顶点。唯一的例外是四面体是简单的封闭测量学，但没有1-vertex quasigeodesic。 我们还确定了一类无限类四面体，每个四面体至少具有34个简单的封闭式准化学。
Pogorelov proved in 1949 that every every convex polyhedron has at least three simple closed quasigeodesics. Whereas a geodesic has exactly pi surface angle to either side at each point, a quasigeodesic has at most pi surface angle to either side at each point. Pogorelov's existence proof did not suggest a way to identify the three quasigeodesics, and it is only recently that a finite algorithm has been proposed. Here we identify three simple closed quasigeodesics on any tetrahedron: at least one through 1 vertex, at least one through 2 vertices, and at least one through 3 vertices. The only exception is that isosceles tetrahedra have simple closed geodesics but do not have a 1-vertex quasigeodesic. We also identify an infinite class of tetrahedra that each have at least 34 simple closed quasigeodesics.
