Geodesic
Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate principal $G$-bundles on a compact Kähler manifold, where $G$ is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it is shown that a principal $G$-bundle $E_G$ admits an Einstein–Hermitian connection if and only if $E_G$ is polystable. We give an equivalent formulation of the (semi)stability condition. A question is to compare this definition with that of [Gómez T. L., Langer A., Schmitt A. H. W., Sols I., Ramanujan Math. Soc. Lect. Notes Ser., Vol. 10, Ramanujan Math. Soc., Mysore, 2010, 281–371].
Keywords: Einstein–Hermitian connection; principal bundle; parabolic subgroup; (semi)stability. 
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     author = {Indranil Biswas and Tom\'as L. G\'omez},
     title = {Semistability of {Principal} {Bundles} on {a~K\"ahler} {Manifold} with {a~Non-Connected} {Structure} {Group}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a12/}
}
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Indranil Biswas; Tomás L. Gómez. Semistability of Principal Bundles on a Kähler Manifold with a Non-Connected Structure Group. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a12/

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