Cartan forms and structure equations

precondition

Could someone explain these two concepts? What I need is the big picture of 'why' we need this, roughly 'what' these equations mean, 'where' its used etc
Thanks in advance

precondition

omg.. nobody answering...
there aren't many people who understand these stuff eh?

Doodle Bob

i think it is more of a matter of complexity. there are entire books written to answer that question.

I'll give the why, you can explore the what on your own: Cartan forms and connections allow us to define differentiation on certain geometrical objects, namely fibre bundles. This topic has proven valuable in constructing models for phenomena in GR and string theory.

Any book on gauge theory and physics will discuss this. for a heavy duty mathematical treatment, look for the book Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems by my friend Tom Ivey.