Geodesic
Yang-Mills bar connections over compact Kähler manifolds
Archivum mathematicum, Tome 46 (2010) no. 1, pp. 47-69.

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In this note we introduce a Yang-Mills bar equation on complex vector bundles $E$ provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on $E$ can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections among a class of Yang-Mills bar connections over compact Käahler manifolds of positive Ricci curvature.
Classification : 53C44, 53C55, 58E99
Keywords: Kähler manifold; complex vector bundle; holomorphic connection; Yang-Mills bar gradient flow 
@article{ARM_2010__46_1_a4,
     author = {V\^an L\^e, H\^ong},
     title = {Yang-Mills bar connections over compact {K\"ahler} manifolds},
     journal = {Archivum mathematicum},
     pages = {47--69},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2010},
     mrnumber = {2644454},
     zbl = {1240.53118},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010__46_1_a4/}
}
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Vân Lê, Hông. Yang-Mills bar connections over compact Kähler manifolds. Archivum mathematicum, Tome 46 (2010) no. 1, pp. 47-69. http://geodesic.mathdoc.fr/item/ARM_2010__46_1_a4/