论文标题
Riemannian指标在GHMC抗DE保姆结构的模量空间上
Riemannian metrics on the moduli space of GHMC anti-de Sitter structures
论文作者
论文摘要
在简短的说明中，我们说明了如何在$ \ mathrm {sl}（3，\ mathbb {r}）上调整两个Riemannian指标的构建$ - Hitchin组件到全球夸张的抗双曲线抗DE安静结构的变形空间：压力指标和Loftin Metric（由Qiongling Li）进行了压力指标。我们表明前者是堕落的，我们表征了其退化的基因座，而后者无处堕落，而fuchsian locus是Teichmüller空间的完全测量的副本，并带有Weil-Petersson的倍数。
In this short note we explain how to adapt the construction of two Riemannian metrics on the $\mathrm{SL}(3,\mathbb{R})$-Hitchin component to the deformation space of globally hyperbolic anti-de Sitter structures: the pressure metric and the Loftin metric (studied by Qiongling Li). We show that the former is degenerate and we characterize its degenerate locus, whereas the latter is nowhere degenerate and the Fuchsian locus is a totally geodesic copy of Teichmüller space endowed with a multiple of the Weil-Petersson metric.
