论文标题
Lorentzian歧管上的本地极端及时的地球循环
Locally Extremal Timelike Geodesic Loops on Lorentzian Manifolds
论文作者
论文摘要
封闭的大地测量学的存在是Riemannian几何形状中经典的，经典的主题，具有许多美丽的结果和强大的技术。但是，在洛伦兹几何形状中，许多在这种情况下运作良好的技术效果远远低。在此处重新审视此问题时，我们介绍了及时的地球同质概念，这是对Lorentzian歧管上时间型循环的更标准时间同型（也称为$ t $ homotophy）的限制。该工具与局部缩短/拉伸长度参数结合使用，以提供有关紧凑型Lorentz歧管上的封闭时间型地球固定的新结果。
Conditions for the existence of closed geodesics is a classic, much-studied subject in Riemannian geometry, with many beautiful results and powerful techniques. However, many of the techniques that work so well in that context are far less effective in Lorentzian geometry. In revisiting this problem here, we introduce the notion of timelike geodesic homotopy, a restriction to geodesics of the more standard timelike homotopy (also known as $t$-homotopy) of timelike loops on Lorentzian manifolds. This tool is combined with a local shortening/stretching of length argument to provide a number of new results on the existence of closed timelike geodesics on compact Lorentz manifolds.
