The Exterior Covariant Derivative: Understanding Connections and Fibre Bundles

[matness]

Can you give me the definition of exterior covariant derivative or any reference web page ?

Wiki does not involve enough info.I am not able to do calculation with respect to given definition there.

Thanks in advance

 

[shoehorn]

The wikipedia article seems relatively complete to me. What specifically don't you understand about it?

 

[matness]

Because the definition of connection in my mind is : "a bilinear connection satisfying certain properties."
I don't know what horizantal/ vertical component mean exactly.
what do "D" to a p-form for example?
I need a definition or explanation using indices at first, because i am trying to understand smt related to physics.

 

[shoehorn]

Because the definition of connection in my mind is : "a bilinear connection satisfying certain properties."

Then it sounds as though you're familiar with the concept of a connection only within the context of a connection on a differentiable manifold. To understand the idea of a covariant exterior connection you'll need to understand the more general idea of a connection over a fibre bundle. It would, in my opinion, be a waste of time to attempt to do what you're asking without even a basic idea of what a connection over a fibre bundle is; to be more precise, you'll need to know what a connection over a $G$-bundle is in order to be able to appreciate the idea of a covariant exterior derivative.

By the way, the "horizontal" and "vertical" bits refer to a decomposition technique used when looking at subspaces over a fibre bundle. Nakahara's book has a decent introduction to this.