论文标题
关于Lorentzian指标的确定的评论
Remarks on the determination of the Lorentzian metric by the lengths of geodesics or null-geodesics
论文作者
论文摘要
我们考虑$ \ Mathbb {r} \ times \ Mathbb {r}^n $中的Lorentzian度量。我们表明，如果我们知道当$ t = 0 $时，我们知道时空测量学的长度为$（0，y，η）$，那么我们可以以$ y $的价格恢复公制。我们证明了洛伦兹指标的刚性。我们还证明了null-Geodesics情况的刚度属性的一种变体：如果两个指标接近，并且相应的零地形学具有相等的欧几里得长度，则指标相等。
We consider a Lorentzian metric in $\mathbb{R}\times\mathbb{R}^n$. We show that if we know the lengths of the space-time geodesics starting at $(0,y,η)$ when $t=0$, then we can recover the metric at $y$. We prove the rigidity of Lorentzian metrics. We also prove a variant of the rigidity property for the case of null-geodesics: if two metrics are close and if corresponding null-geodesics have equal Euclidian lengths then the metrics are equal.
