论文标题
Lorentzian指标的刚度与无效的时间相同
Rigidity for Lorentzian metrics with the same length of null-geodesics
论文作者
论文摘要
我们研究了Lorentzian度量，独立于气缸$ \ mathbb {r} \timsΩ$中的时间变量，其中$ x_0 \ in \ mathbb {r} $是时间变量，而$ω$是$ \ m athbb {r}^n $ in $ \ mathbb {r}^n $。我们考虑在$ \ Mathbb {r} \ timesω$上以$ \ mathbb {r} \ times \ times \partialΩ$ at $ t = 0 $启动的前向null-geodesics，然后在后来的某个时候离开$ \ times \partialΩ$。我们证明了以下刚度结果：如果两个洛伦兹指标在某些规范上足够接近，并且相应的无偏格学具有相等的长度，则指标相等。
We study the Lorentzian metric independent of the time variable in the cylinder $\mathbb{R}\timesΩ$ where $x_0\in\mathbb{R}$ is the time variable and $Ω$ is a bounded smooth domain in $\mathbb{R}^n$. We consider forward null-geodesics in $\mathbb{R}\times Ω$ starting on $\mathbb{R}\times\partialΩ$ at $t=0$ and leaving $\mathbb{R}\timesΩ$ at some later time. We prove the following rigidity result: If two Lorentzian metrics are close enough in some norm and if corresponding null-geodesics have equal lengths then the metrics are equal.
