Yang-Mills bar connection and holomorphic structure  

Yang-Mills bar联络与全纯结构

作　　者：Teng Huang 黄腾(中国科学技术大学数学科学学院,中国科学院吴文俊数学重点实验室,安徽合肥230026)

机构地区：[1]Wu Wen-Tsun Key Laboratory of Mathematics,Chinese Academy of Sciences,School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《中国科学技术大学学报》2024年第8期2-5,1,I0002,共6页JUSTC

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.

摘　　要：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.研究了紧致复流形X上G-主丛P的Yang-Mills bar联络A,即A的曲率满足方程δ_(A)^(*)F_(A)^(0.2)。由Koszul-Malgrange准则可知P上的任何全纯结构都是该方程的解。当G=SU(2)或SO(3)以及X是一个复曲面且H_(1)(X,Z_(2))=0时,我们可以证明不可约的Yang-Mills bar联络的(0,2)-曲率部分是消失的,即(P,δ_(A))此时是全纯的。

关 键 词：Yang-Mills bar connection holomorphic structure Kähler surface 

分 类 号：O186[理学—数学]