ABSTRACT
11.1 Proposition Let π : P → M be a principal G-bundle with a connection form ω, and let H be a Lie subgroup of G so that https://www.w3.org/1998/Math/MathML"> g = h ⊗ W https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315366722/660a41ec-09ea-4535-a2aa-9fc9a667124f/content/un11_e001.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> for a subspace W of g with Ad(H) (W) ⊂ W. If π′: Q → M is a reduced subbundle of π : P → M with structure group H, and if i: Q → P is the inclusion map and ρ: g → h is the projection on h, then ρ • i*(ω) is a connection form on Q.
