Bergman metric

In differential geometry, the Bergman metric is a Hermitian metric that can be defined on certain types of complex manifold. It is so called because it is derived from the Bergman kernel, both of which are named for Stefan Bergman.

Let ${\displaystyle G\subset {\mathbb {C} }^{n}}$ be a domain and let ${\displaystyle K(z,w)}$ be the Bergman kernel on G. We define a Hermitian metric on the tangent bundle ${\displaystyle T_{z}{\mathbb {C} }^{n}}$ by

...
Wikipedia