I am exploring the concepts of connection forms and the transport theorem in differential geometry. I understand that a connection form organizes the data of a connection using moving frames and differential forms.
My question is: Is there a way to connect the notion of the connection form with the transport theorem? Specifically, how does the connection form facilitate the derivation of the transport theorem, and what role does it play in describing the rate of change of a vector field along a curve?
Any explanations or references to relevant literature would be greatly appreciated!
