Event description
A Hermitian metric g on a complex manifold (M, J) is said to be Kähler if its fundamental 2-form ω is closed, to be pluriclosed or SKT if the torsion of the associated Bismut connection ∇^B is d-closed, and is called balanced if its fundamental 2-form is d^∗-closed or its Lee 1-form θ vanishes identically. We present an overview of recent results on pluriclosed and balanced metrics, provide various examples of non-Kähler manifolds and also present some open problems in the field of Complex Geometry, based on the survey [1] by Prof.ssa Anna Fino.
[1] A. Fino. Canonical metrics in complex geometry. Bollettino dell’Unione Matematica Italiana, 18 (2025)
[2] J. M. Lee. Introduction to Complex Manifolds. American Mathematical Society, 244 (2024).