Canonical Metrics in Complex Geometry

Explore canonical metrics in complex geometry through this 55-minute lecture by Anna Fino from Florida International University. Delve into the importance of canonical metrics as tools for studying complex non-Kähler manifolds, focusing on pluriclosed and balanced metrics. Examine the properties of Hermitian metrics, including pluriclosed metrics with closed torsion of the Bismut connection and balanced metrics with co-closed fundamental forms. Discover general results and new constructions of compact non-Kähler manifolds. Investigate the relationship between pluriclosed metrics, generalized Hermitian structures, and generalized Kähler structures.