Natural connections on Stiefel bundles are sourceless gauge fields

Abstract
It is shown that the natural connections defined on real and complex Stiefel bundles over Grassmannian manifolds are sourceless gauge fields corresponding to the gauge groups G=SO(k), k=2,3,⋅⋅⋅ and U(k), k=1,2,⋅⋅⋅, respectively. Stiefel bundles and their connections are important in view of their universality: Any gauge field, with group G, defined on a compact manifold may be obtained by embedding the manifold in a Grassmannian of sufficiently high dimension.

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