Hermitian Yang–Mills Connection

(Differential Geometry)


Differential Geometry since 1980
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What is Hermitian Yang–Mills connection?

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. The Kobayashi–Hitchin correspondence proved by Donaldson, Uhlenbeck and Yau asserts that a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian Yang–Mills connection if and only if it is slope polystable.

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albert einsteindifferential geometrypartial differential equationvector bundle


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Sources: DBpedia
 — Date merged: 11/6/2021, 1:32:46 PM
 — Date scraped: 5/20/2021, 5:47:23 PM