Basic 1-Forms on Principal Fiber Bundles
Thursday, April 25, 2013
This Exercise is a simple specialization of the general criterion stated in the paragraph 6.38 of the TextBook for basic 1-forms on principal fiber bundles. 
It shows that a 1-form on the total space of a principal fiber bundle is basic, that is, is the pullback of a 1-form of the base space of the bundle, if and only if the 1-form vanishes on the fibers of the bundle and is invariant by the action of the structure goup.  Ref.