Kähler manifold
Hermite-Einstein connections arise as solutions of the Hermitian Yang-Mills equations. These are a system of partial differential equations on a vector bundle over a Kähler manifold, which imply the Yang-Mills equations. Let formula_1 be a Hermitian connection on a Hermitian vector bundle formula_2 over a Kähler manifold formula_3 of dimension formula_4. Then the Hermitian Yang-Mills equations are