Constant scalar curvature Kähler metric

In differential geometry, a constant scalar curvature Kähler metric (cscK metric), is (as the name suggests) a Kähler metric on a complex manifold whose scalar curvature is constant.

Donaldson (2002), Tian and Yau conjectured that the existence of a cscK metric on a manifold is equivalent to the manifold being stable in some sense.