Abstract
Let \(\overline M \) be a compact complex manifold of complex dimension two with a smooth Kähler metric and D a smooth divisor on \(\overline M \). If E is a rank 2 holomorphic vector bundle on \(\overline M \) with a stable parabolic structure along D, we prove the existence of a metric on \(E'{\text{ = }}E|_{\overline M \backslash D} \) (compatible with the parabolic structure) which is Hermitian-Einstein with respect to the restriction of the Kähler metric to \(\overline M \)ĚD. A converse is also proved.
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Li, J., Narasimhan, M.S. Hermitian-einstein metrics on parabolic stable bundles. Acta Math Sinica 15, 93–114 (1999). https://doi.org/10.1007/s10114-999-0062-8
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DOI: https://doi.org/10.1007/s10114-999-0062-8