In this note,we study the Yang-Mills bar connection,i.e.,the curvature of obeys,δ_(A)^(*)F_(A)^(0.2)on a principal G-bundle P over a compact complex manifold.According to the Koszul-Malgrange criterion,any holomorphi...In this note,we study the Yang-Mills bar connection,i.e.,the curvature of obeys,δ_(A)^(*)F_(A)^(0.2)on a principal G-bundle P over a compact complex manifold.According to the Koszul-Malgrange criterion,any holomorphic structure on can be seen as a solution to this equation.Suppose that G=SU(2)or SO(3)and X is a complex surface with H_(1)(X,Z_(2))=0.We then prove that the-part curvature of an irreducible Yang-Mills bar connection vanishes,i.e.,(P,δ_(A))is holomorphic.展开更多
基金supported by the National Natural Science Foundation of China(12271496)the Youth Innovation Promotion Association CAS,the Fundamental Research Funds of the Central Universities,and the USTC Research Funds of the Double First-Class Initiative.
文摘In this note,we study the Yang-Mills bar connection,i.e.,the curvature of obeys,δ_(A)^(*)F_(A)^(0.2)on a principal G-bundle P over a compact complex manifold.According to the Koszul-Malgrange criterion,any holomorphic structure on can be seen as a solution to this equation.Suppose that G=SU(2)or SO(3)and X is a complex surface with H_(1)(X,Z_(2))=0.We then prove that the-part curvature of an irreducible Yang-Mills bar connection vanishes,i.e.,(P,δ_(A))is holomorphic.
