Hermitian-Einstein metrics from noncommutative $U\left(1\right)$ instantons

Kentaro Hara, Akifumi Sako, Hyun Seok Yang

We show that Hermitian-Einstein metrics can be locally constructed by a map from (anti-)self-dual two-forms on Euclidean ${\mathbb{R}}^4$ to symmetric two-tensors introduced in "Gra…