Abstract
The authors show that a unipotent vector bundle on a non–Kähler compact complex manifold does not admit a flat holomorphic connection in general. It was also construct examples of topologically trivial stable vector bundle on compact Gauduchon manifold that does not admit any unitary flat connection.
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Biswas, I., Florentino, C. A remark on “Connections and Higgs fields on a principal bundle”. Ann Glob Anal Geom 40, 287–289 (2011). https://doi.org/10.1007/s10455-011-9257-1
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DOI: https://doi.org/10.1007/s10455-011-9257-1