Li, Jiayu et S. Narasimhan, M., Hermitian-einstein metrics on parabolic stable bundles, Acta mathematica Sinica. English series (Print) , 15(1), 1999, pp. 93-114
Let M..... be a compact complex manifold of complex dimension two with a smooth Kähler metric and D a smooth divisor on M...... If E is a rank 2 holomorphic vector bundle on M..... with a stable parabolic structure along D, we prove the existence of a metric on E. = E|M.......D (compatible with the parabolic structure) which is Hermitian-Einstein with respect to the restriction of the Kähler metric to M......D. A converse is also proved.