Geodesic
A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a Riemann surface
Documenta mathematica, Tome 18 (2013), pp. 111-120
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Let EG​ be a holomorphic principal G-bundle over a compact connected Riemann surface, where G is a connected reductive affine algebraic group defined over C, such that EG​ admits a holomorphic connection. Take any β∈H0(X,ad(EG​)), where ad(EG​) is the adjoint vector bundle for EG​, such that the conjugacy class β(x)∈g/G,x∈X, is independent of x. We give a sufficient condition for the existence of a holomorphic connection on EG​ such that β is flat with respect to the induced connection on ad(EG​).
DOI : 10.4171/dm/393
Classification : 14H60, 53C07
Mots-clés : holomorphic connection, adjoint bundle, flatness, canonical connection 
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     author = {Indranil Biswas},
     title = {A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a {Riemann} surface},
     journal = {Documenta mathematica},
     pages = {111--120},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/393},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/393/}
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Indranil Biswas. A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a Riemann surface. Documenta mathematica, Tome 18 (2013), pp. 111-120. doi: 10.4171/dm/393

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