Connection Forms Associated To A Principal Connection
Conversely, a principal G-connection ω in a principal G-bundle P→M gives rise to a collection of connection forms on M. Suppose that e : M → P is a local section of P. Then the pullback of ω along e defines a g-valued one-form on M:
Changing frames by a G-valued function g, one sees that ω(e) transforms in the required manner by using the Leibniz rule, and the adjunction:
where X is a vector on M, and d denotes the pushforward.
Read more about this topic: Connection Form, Principal Bundles
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