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Stability of Einstein-Hermitian vector bundles. (English) Zbl 0558.53037
On a compact Kähler manifold there is a close relationship between stable bundles in the sense of Mumford-Takemoto and the Einstein- Hermitian vector bundles of S. Kobayashi [Einstein-Hermitian vector bundles and stability, Proc. Sympos. Global Riemannian Geometry, Durham, England 1982]. These Einstein-Hermitian bundles are Hermitian vector bundles with a certain restriction on their curvature.
In this paper the author proves a theorem announced by Kobayashi: An Einstein-Hermitian bundle on a compact Kähler manifold is semi-stable and a direct sum of stable Einstein-Hermitian line bundles. The proof is short and efficient.
Reviewer: M.G.Eastwood

MSC:
53C55 Global differential geometry of Hermitian and Kählerian manifolds
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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