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Deriving covariant differention formula on covectors from the formula on vectors.

  1. Oct 9, 2014 #1
    For a vector : ##\nabla_a V^b=\partial _a V^b+T^b_{ac}V^c##

    I am trying to derive for a covector: ##\nabla_a w_b=\partial _a w_b+T^c_{ab}w_c##

    I am told to use the Leibniz Rule and the definition that for a scalar ##f## : ##\nabla_a f =\partial_a f ## to do so

    My thoughts:

    Define ##w_b## through the ##\nabla ## function: ##w_b##= ##\nabla _b f ##

    And I'm not sure what my next move should be.

    Many Thanks for any help in advance !
     
  2. jcsd
  3. Oct 9, 2014 #2
    Is it not possible to edit threads anymore?
    Second eq should be a neg sign before T .. !
     
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