 Kähler–Einstein metric

A Kähler-Einstein metric is a special type of Riemannian metric that arises in differential geometry and algebraic geometry. It is associated with Kähler manifolds, which are a class of complex manifolds with a compatible symplectic structure. A Kähler manifold is a complex manifold \( (M, J) \) equipped with a Kähler metric \( g \), which is a Riemannian metric that is both Hermitian and symplectic.