AI 中文总结
该研究针对厄米特几何中与陈联络标量曲率相关的三个问题，以典范度量的识别与构造为目标，选取偏微分方程分析、动量映射、变分方法三类技术交互的范例展开探讨。
AI 中文摘要
我们描述了厄米特几何中与陈联络标量曲率相关的三个问题，旨在识别和构造典范度量，这些问题被选为不同技术自然交互的范例，涉及偏微分方程的分析方法、动量映射概念以及变分方法。
英文摘要
We describe three problems in Hermitian geometry related to the scalar curvature of the Chern connection, aimed at identifying and constructing canonical metrics. They are chosen as toy examples where different techniques naturally interact: analytic methods for partial differential equations, the notion of momentum map, and variational methods.
CommentsThese notes were prepared for the course delivered by the author at the CIME Summer School "Cohomological properties of almost complex manifolds and special structures", held in Cetraro (CS), July 13--17, 2026
