Constant scalar curvature Kähler metric

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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. A special case is Kähler-Einstein metric, and a more general case is extremal Kähler metric.

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.