In this article we define new flows on the Hitchin components for \(\mathrm {PGL}(V)\). Special examples of these flows are associated to simple closed curves on the surface and give generalized twist flows. Other examples, so called eruption flows, are associated to pair of pants in S and capture new phenomena which are not present in the case when \(n=2\). We determine a global coordinate system on the Hitchin component. Using the computation of the Goldman symplectic form on the Hitchin component, that is developed by two of the authors in a companion paper to this article (Sun and Zhang in The Goldman symplectic form on the \(\mathrm{PGL} ({V})\)-Hitchin component, 2017. arXiv:1709.03589), this gives a global Darboux coordinate system on the Hitchin component.

中文翻译：

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$$ \ mathbf {PGL（V）} $$ PGL（V）-Hitchin组件上的流

在本文中，我们在Hitchin组件上为\（\ mathrm {PGL}（V）\）定义了新流程。这些流动的特殊示例与表面上的简单闭合曲线相关，并给出了广义的扭曲流动。其他示例，即所谓的喷发流，与S中的一条裤子相关联，并捕获了在\（n = 2 \）情况下不存在的新现象。我们在Hitchin组件上确定一个全局坐标系。使用两位作者在与本文相伴的文章中开发的Hitchin分量上的高盛辛形式进行计算（Sun和Zhang在\（\ mathrm {PGL}（{V} ）\）-Hitchin组件，2017年。arXiv：1709.03589），这会在Hitchin组件上提供一个全局的Darboux坐标系。