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A Notation in Ricci form

  1. Oct 17, 2016 #1
    The material I am studying express the Ricci form as
    ##R = i{R_{\mu \bar \nu }}d{z^\mu } \wedge d{{\bar z}^\nu } = i\partial \partial \log G##
    where ##G## is the determinant of metric tensor, but I am not sure what does ##\log G## here, can anybody help?
     
  2. jcsd
  3. Oct 17, 2016 #2

    Ben Niehoff

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    G is the determinant of the metric (the Riemannian metric, or the Hermitian metric? Pretty sure the latter, but it makes a difference). And log G is its logarithm. What part of it is confusing?
     
  4. Oct 18, 2016 #3
    Thanks for replying. Basically I was trying to ask the defintion of logarithm of matrix when I was looking at the definition of Ricci form. The example I posted there is not a good one.
     
  5. Oct 19, 2016 #4

    Ben Niehoff

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    But there is no logarithm of a matrix in the formula you posted. It's the logarithm of the determinant of a matrix.
     
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