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
In this paper,we study the curvature estimate of the Hermitian–Yang–Mills flow on holomorphic vector bundles.In one simple case,we show that the curvature of the evolved Hermitian metric is uniformly bounded away fr...In this paper,we study the curvature estimate of the Hermitian–Yang–Mills flow on holomorphic vector bundles.In one simple case,we show that the curvature of the evolved Hermitian metric is uniformly bounded away from the analytic subvariety determined by the Harder–Narasimhan–Seshadri filtration of the holomorphic vector bundle.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.
基金supported in part by NSF in China,Nos.11625106,11571332,and 11721101.
文摘In this paper,we study the curvature estimate of the Hermitian–Yang–Mills flow on holomorphic vector bundles.In one simple case,we show that the curvature of the evolved Hermitian metric is uniformly bounded away from the analytic subvariety determined by the Harder–Narasimhan–Seshadri filtration of the holomorphic vector bundle.
