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Exterior covariant derivative

  1. Jul 17, 2008 #1
    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
     
  2. jcsd
  3. Jul 17, 2008 #2
    The wikipedia article seems relatively complete to me. What specifically don't you understand about it?
     
  4. Jul 17, 2008 #3
    Because the definition of connection in my mind is : "a bilinear connection satisfying certain properties."
    I dont 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.
     
  5. Jul 17, 2008 #4
    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 [itex]G[/itex]-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.
     
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