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Hermitian-einstein metrics on parabolic stable bundles
Authors:Jiayu Li  M S Narasimhan
Institution:(1) Institute of Mathematics, Academia Sinica, 100080 Beijing, P. R. China;(2) Mathematics Section, International Centre for Theoretic Physics, P.O.Box 586, 34100 Trieste, Italy
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.
Keywords:Hermitian-Einstein metric  Parabolic stable bundle  K?hler manifold
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