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Covariant derivative

  1. Jan 14, 2010 #1
    Hello everyone,

    While studying properties of Riemann and tensor and Killing vectors, I found this notation/concept that I'm not sure of it's meaning.

    What does it mean to have a covariant derivative, using semi-colon notation, showing in upper index position. Is it just a matter of raising the index via the metric of ordinary covariant derivative.

    I tried to search in different textbooks for this, but couldn't find anything.

    Thanks in advance for your help.
  2. jcsd
  3. Jan 14, 2010 #2

    Ben Niehoff

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    Gold Member

    [tex]A^{ab;c} = g^{cd} \nabla_d A^{ab} = \nabla_d (g^{cd} A^{ab})[/tex]

    Note that [itex]\nabla_c g_{ab} = 0[/itex].
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