Stability of Einstein-Hermitian vector bundles
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 \textit{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.
scientific article; zbMATH DE number 3890301