A necessary and sufficient condition is given for parabolic vector bundles on Riemann surfaces to admit parabolic Lie algebroid connections.
Tortella, -modules and holomorphic Lie algebroids , PhD thesis, Scuola Internazionale Superiore di Studi Avanzati (2011)
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A criterion for parabolic vector bundles to admit a parabolic Lie algebroid connection
A necessary and sufficient condition is given for parabolic vector bundles on Riemann surfaces to admit parabolic Lie algebroid connections.