Talk:Torsion tensor

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Contents 1 Understanding 2 non-sense 3 Move to torsion (differential geometry)? 4 Some other things to think about 5 Does torsion only describe twisting?

[edit] Understanding

I think I'm starting to understand this. Does this accurately describe torsion?:

Suppose you are in the day-to-day flat 3-D universe in a space ship just to the left of someone else in another spaceship, both of you facing in the same direction. If you both move forward that person remains just to your right.

• If you were not in flat space, but you were in torsion-free space, as you both move forward, the person next to you might move further away, but if you only took a small step forward, the other person would still be just to your right.
• In contrast, if the universe were flat but not torsion-free, as you moved forward, the other person would be just as far away, but might appear to orbit you, so that after some distance the other person would appear to be above you.

Is that an accurate description of torsion? —Ben FrantzDale 23:01, 28 April 2007 (UTC)

[edit] non-sense

The following makes no sense:

The components of the torsion tensor T^c_ab can be derived by setting X = e_a,Y = e_b and by introducing the commutator coefficients given by . We finally obtain a component expression of the torsion tensor,

T^c_ab: = Γ^c_ab − Γ^c_ba − γ^c_ba

It implies X=Y which is just silly. If I stretch my imagination a bit then γ might be meant to be simply [X, Y] which would make this the component version of the tensorial definition. Someone should fix or remove this. --MarSch 10:32, 20 May 2007 (UTC)

I agree that the statement was a little odd. The author clearly intended a and b to signify numerical indices of the frame (rather than abstract indices). This is the only interpretation where you can have X ≠ Y. Anyway, feel free to do with it as you like. Physicists, I believe, generally use Latin subscripts such as i,j,k,... (or sometimes Greek indices) for numerical indices as opposed to the letters from the beginning of the alphabet such as a,b,etc. I have preserved the notation, but perhaps it would be a good idea to bring it in line with prevailing conventions. Silly rabbit 11:48, 20 May 2007 (UTC)

[edit] Move to torsion (differential geometry)?

I propose moving this to torsion (differential geometry), currently a redirect here. That way the article can discuss torsion in a slightly broader context than just the torsion tensor (torsion form, intrinsic and extrinsic torsion, torsion of a prolongation, etc.) Silly rabbit 12:30, 20 May 2007 (UTC)

Probably a good idea. --MarSch 13:34, 20 May 2007 (UTC)

I agree to move this article to torsion (differential geometry). Then let's merge torsion of curves to the moved article. --Acepectif 03:20, 31 August 2007 (UTC)

[edit] Some other things to think about

• Torsion of almost complex structures: The Nijenhuis tensor.
• The torsion of a hermitian connection vanishes if and only if the manifold is Kähler.
• Analytic torsion and the Weitzenbock identity.
• Torsion of Cartan connections.
• Weyl geometries and projective connections.

Silly rabbit 16:12, 8 June 2007 (UTC)

[edit] Does torsion only describe twisting?

My understanding is that expansion or contraction of a frame as it moves along a curve is also torsion. Is this wrong, or does the description of torsion need revision? 81.79.139.224 (talk) 07:29, 20 April 2008 (UTC)