A criterion for the existence of a flat connection on a parabolic vector bundle

Biswas, Indranil (2002) A criterion for the existence of a flat connection on a parabolic vector bundle Advances in Geometry, 2 (3). pp. 231-241. ISSN 1615-715X

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Abstract

We define holomorphic connection on a parabolic vector bundle over a Riemann surface and prove that a parabolic vector bundle admits a holomorphic connection if and only if each direct summand of it is of parabolic degree zero. This is a generalization to the parabolic context of a well-known result of Weil which says that a holomorphic vector bundle on a Riemann surface admits a holomorphic connection if and only if every direct summand of it is of degree zero.

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Deposited On:12 Oct 2010 04:34
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