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I'm trying to think of the curvature form of a connection on a tangent frame pricipal bundle as an alternative description of the Riemannian curvature of the connection(see i.e. https://en.wikipedia.org/wiki/Curvature_form)
One thing I want to confirm is does a non-vanishing curvature-form imply loss of the information about the vector direction when parallel transporting it like in the Riemannian curvature case?
One thing I want to confirm is does a non-vanishing curvature-form imply loss of the information about the vector direction when parallel transporting it like in the Riemannian curvature case?