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Affine connection Γ in terms of tetrad

  1. Nov 14, 2015 #1
    Hi, some one know the expression of the affine connection Γ in terms of tetrad formalism? I would like also some references if it's possible, i found a hit but i think that is wrong... please help me it's so important!
     
  2. jcsd
  3. Nov 14, 2015 #2
    $$Γ^{\lambda} _{μν} = \frac{1}{2} (e^κ ⋅ e^λ) ( ∂_μ (e_κ ⋅ e_ν) + ∂_ν (e_κ⋅e_μ) - ∂_κ (e_μ⋅e_ν))$$
     
  4. Nov 14, 2015 #3
    I'm loking for this relation:
    \begin{equation}
    \Gamma^c_{ab}=-\Omega_{ab}\,^c+\Omega_b\,^c\,_a-\Omega^c\,_{ab} \end{equation}
    where $\Omega$ is:
    \begin{equation}
    \Omega_{ab}\,^c=e^\mu\,_ae^\nu\,_b\partial_{[\mu}e_{\nu]}\,^c
    \end{equation}
    But i have an extra term and i don't understand where is the mistake
     
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