Abstract

In recent years, there has been growing interest in the study of (not necessarily Kähler) Hermitian manifolds: complex manifolds endowed with a compatible Riemannian metric. On a generic Hermitian manifold, the complex structure is not compatible with the Levi-Civita connection. Instead, one wishes to study the geometry of Hermitian connections - those compatible with both the complex structure and metric. In the 90's, Gauduchon introduced a "canonical" one dimensional subspace of Hermitian connections. In this talk, we will discuss some recent results regarding the curvature properties of these Gauduchon connections. In particular, we will present the classification of those compact Hermitian manifolds with flat Gauduchon connection by confirming a conjecture of Yang and Zheng. Also, we will discuss some recent progress on the associated Ricci and Holomorphic sectional curvatures. This is based on several joint works with Kyle Broder and Ramiro Lafuente.

Afternoon tea will be provided.