James Stanfield: Hermitian manifolds with flat Gauduchon connections

On a generic Hermitian manifold (A complex manifold with compatible Riemannian metric), the complex structure is not compatible with the Levi-Civita connection. Instead, one considers metric connections that are compatible with the complex structure, but which have torsion. In the 90's, Gauduchon introduced a "canonical" one dimensional subspace which included all previously distinguished Hermitian connections (in particular, the Chern and Bismut connections). In this talk, we will discuss some recent results regarding the curvature properties of these connections. In particular, we will present the classification of compact Hermitian manifolds with flat Gauduchon connection by confirming a conjecture of Yang and Zheng. This is based on joint work with Ramiro Lafuente.

Видео James Stanfield: Hermitian manifolds with flat Gauduchon connections канала Australian Geometric PDE Seminar