论文标题
Lorentz-Finsler关于符号和接触转化组的指标
Lorentz-Finsler metrics on symplectic and contact transformation groups
论文作者
论文摘要
在这些注释中，我们讨论了洛伦兹 - 芬斯勒指标，这是一个起源于相对论的概念，这些概念是在某些符号和接触转换组上的。在这种情况下引起的一些基本几何问题，涉及距离，大地测量及其共轭点以及时间函数的存在，事实证明与各种主题有关，包括接触收缩期问题，群体准疗法，Monge-Ampère方程以及符合性刚性和灵活性之间的微妙相互作用。我们讨论这些相互关系，提供必要的初步，并提出许多空旷的问题。
In these notes we discuss Lorentz-Finsler metrics, a notion originated in relativity theory, on certain groups of symplectic and contact transformations. Some basic geometric questions arising in this context concerning distance, geodesics and their conjugate points, and existence of a time function, turn out to be related to a variety of subjects including the contact systolic problem, group quasi-morphisms, the Monge-Ampère equation, and a subtle interplay between symplectic rigidity and flexibility. We discuss these interrelations, providing necessary preliminaries, and formulate a number of open questions.
