The unitary connections on the complex Grassmann manifold期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The unitary connections on the complex Grassmann manifold

Authors:

Institution:

(1) Institute of Mathematics, Chinese Academy of Sciences, 100080 Beijing, China;(2) Institute of Mathematics, Shantou University, 515063 Shantou, China

Abstract:

In the complex Grassmann manifold ℱ(m,n), the space of complexn-planes passes through the origin of C^m+n; the local coordinate of the space can be arranged into anm ×n matrixZ. It is proved that

$K = K(Z,dZ) = (I + ZZ^\dag )^{ - \frac{1}{2}\overline \partial } (I + ZZ^\dag )^{\frac{1}{2}} - \partial (I + ZZ^\dag )^{\frac{1}{2}} + (I + ZZ^\dag )^{ - \frac{1}{2}}$

is a U(m)-connection of ℱ(m,n) and its curvature form

$\Omega _1 = dK + K\Lambda K$

satisfies the Yang-Mills equation. Moreover,

$B = B(Z,{\bf{ }}dZ) = K(Z,{\bf{ }}dZ) - \frac{{tr(K(Z,{\bf{ }}dZ))}}{m}I^{(m)}$

is an (Sum)-connection and its curvature form

$\Omega _2 = dB + B{\bf{ }}\Lambda {\bf{ }}B$

satisfies the Yang-Mills equation. Project partially supported by the National Natural Science Foundation of China (Grant No. 19631010) and Fundamental Research Bureau of CAS.

Keywords:

unitary connection Grassmann manifold

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏