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- W2963713736 abstract "Here c1(E, h) is the first Chern form of E with respect to a Hermitian metric h. The famous theorem of Donaldson [7, 8] (for algebraic manifolds only) and Uhlenbeck-Yau [24, 25] says that an irreducible vector bundle E → N is ω-stable if and only if it admits a HermitianEinstein metric (i.e. a metric whose curvature, when the 2-form part is contracted with the metric on N , is a constant times the identity endomorphism on E). This correspondence between stable bundles and Hermitian-Einstein metrics is often called the Kobayashi-Hitchin correspondence. An important generalization of this theorem is provided by Li-Yau [15] for complex manifolds (and subsequently due to Buchdahl by a different method for surfaces [3]). The major insight for this extension is the fact that the degree is well-defined as long as the Hermitian form ω on N satisfies only ∂∂ωn−1 = 0. This is because" @default.
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- W2963713736 date "2009-01-01" @default.
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- W2963713736 title "Affine Hermitian-Einstein Metrics" @default.
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- W2963713736 doi "https://doi.org/10.4310/ajm.2009.v13.n1.a6" @default.
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