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Einstein–Hermitian vector bundle
In differential geometry, an Einstein–Hermitian vector bundle is a Hermitian vector bundle over a Hermitian manifold whose metric is an Einstein–Hermitian metric, meaning that it satisfies the Einstein condition that the mean curvature, considered as an endomorphism of the vector bundle, is a constant times the identity operator. Einstein–Hermitian vector bundles were introduced by .
The Kobayashi–Hitchin correspondence implies that Einstein–Hermitian vector bundles are closely related to stable vector bundles. For example, every irreducible Einstein–Hermitian vector bundle over a compact Kähler manifold is stable.
==See also==
*Einstein manifold
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