Lorentzian angles and trigonometry including lightlike vectors

Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors

Lorentzian manifolds with parallel spinors are important objects of study in several branches of geometry, analysis and mathematical physics. Their Cauchy problem has recently been discussed by Baum, Leistner and Lischewski, who proved that the problem locally has a unique solution up to diffeomorphisms, provided that the intial data given on a space-like hypersurface satisfy some constraint equations. In this article we provide a method to solve these constraint equations. In particular, any curve (resp. closed curve) in the moduli space of Riemannian metrics on $M$ with a parallel spinor giv…

来自类光测地线的全局洛伦兹几何：(2+1)维引力中的观测者能看到什么？

Global Lorentzian geometry from lightlike geodesics: What does an observer in (2+1)-gravity see?

该研究针对(2+1)维引力中平坦洛伦兹3维流形的几何重构问题，提出通过观测者测量返回光线的固有时、方向及频移，即可在有限时间内重构和乐变量与全局几何。

Limit curve theorems in Lorentzian geometry

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causa…

锥结构中的类光超曲面与时间最小测地线

Lightlike hypersurfaces and time-minimizing geodesics in cone structures

本文将洛伦兹几何中的类光超曲面概念推广到无度规的锥结构，证明其具有唯一锥测地线叶状结构，并借此在全局双曲时空中获得锥测地线的时间最小化性质。

Towards a closed differential aging formula in special relativity

It is well known that the Lorentzian length of a timelike curve in Minkowski spacetime is smaller than the Lorentzian length of the geodesic connecting its initial and final endpoints. The difference is known as the 'differential aging' and its calculation in terms of the proper acceleration history of the timelike curve would provide an important tool for the autonomous spacetime navigation of non-inertial observers. I give a solution in 3+1 dimensions which holds whenever the acceleration is decomposed with respect to a lightlike transported frame (lightlike transport will be defined), the a…