Holonomy on the principal $U(n)$ bundles over Grassmannian manifolds

Taechang Byun, Younggi Choi

Consider the principal $U(n)$ bundles over Grassmann manifolds $U(n)\to U(n+m)/U(m)\stackrel{\pi }{\to }{G}_{n,m}$. Given $X\in U_{m,n}(\mathbb{C})$ and a 2-dimensional su…