Hermitian Yang–Mills connection
A HERMITIAN HOLOMORPHIC VECTOR BUNDLE OVER A KÄHLER MANIFOLD, WHOSE CHERN CONNECTION’S CURVATURE SATISFIES EINSTEIN’S EQUATIONS (I.E. EQUALS THE IDENTITY TIMES A CONSTANT)
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In mathematics, and in particular gauge theory and complex geometry, a Hermitian Yang–Mills connection (or Hermite-Einstein connection) is a Chern connection associated to an inner product on a holomorphic vector bundle over a Kähler manifold that satisfies an analogue of Einstein's equations: namely, the contraction of the curvature 2-form of the connection with the Kähler form is required to be a constant times the identity transformation. Hermitian Yang–Mills connections are special examples of Yang–Mills connections, and are often called instantons.