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E α β γ δ = g α ζ g β η g γ θ g δ ι E ζ η θ ι . displaystyle E^ alpha beta gamma delta =g^ alpha zeta g^ beta eta g^ gamma theta g^ delta iota E_ zeta eta theta iota ,.

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Over a pseudo-Riemannian manifold, one could outline a coordinate-invariant covariant tensor field whose coordinate representation agrees Along with more here the Levi-Civita image where ever the coordinate program is these that The premise of your tangent space is orthonormal with respect to your metric and matches a specific orientation.

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The subsequent are samples of the final id above specialised to Minkowski space (Using the adverse indicator arising through the odd variety of negatives while in the signature on the metric tensor in both indication Conference):

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