Almost-Hermitian and Hermitian metrics

Abstract

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.

arXiv commentThese 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