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  1.  
    I've been participating in the discussion on

    http://mathoverflow.net/questions/87491/definition-of-hessian-with-respect-to-connection

    but I do consider this to be too elementary for MO. Am I wrong?
  2.  

    Connections might be very elementary, but they are confusing as hell. I think the question isn't less inappropriate here than it would be on M.SE.