2011/09/27 by Indranil Biswas, Biswas, Indranil, John Loftin +1 · 1 citation
Mathematics · #53C07 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.DG #msc:53C07
paper · pdf · doi:10.48550/arxiv.1109.5808
Final version; to appear in International Journal of Mathematics
arxiv created 2011/09/27 · openalex publication_date 2011/09/27 · arxiv updated 2011/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric g and a covariant constant volume form. Let G be either a connected reductive complex linear algebraic group or the real locus of a split real form of a complex reductive group. We prove that a flat principal G-bundle EG over M admits a Hermitian-Einstein structure if and only if EG is polystable. A polystable flat principal G--bundle over M admits a unique Hermitian-Einstein connection. We also prove the existence and uniqueness of a Harder-Narasimhan filtration for flat vector bundles over M.