JanBielawski

Hi Jan, I've noticed the same spacing (as on the curvature form page) as the standard for the Christoffel symbols here and was wondering - why do we do that here? Does something like $\omega _{j}^{i}$ display badly on your browser? Orthografer 06:13, 11 August 2006 (UTC)

Hello Ortho — $\omega _{j}^{i}$ displays fine, it's just not really proper tensor notation because the indices must come in a definite order, and with $\textstyle i$ sitting exactly above $\textstyle j$ it's not clear which index is first. Putting it differently, $\omega _{\ j}^{i}$ and $\omega _{k}^{\ l}$ are different tensors: $\omega _{\ j}^{i}=g^{ik}g_{jl}\,\omega _{k}^{\ l}\neq \omega _{k}^{\ l}$ This problem does not arise with Christoffel symbols because they are not a tensor and their indices are never raised or lowered. JanBielawski 09:08, 13 August 2006 (UTC)

Thanks, Jan. Orthografer 19:03, 15 August 2006 (UTC)

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