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Results tagged with torsion
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user 613
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What is torsion in differential geometry intuitively?
In any case, at least in the context of Riemannian geometry, what's geometrically natural is zero torsion, so it's not surprising that a geometric interpretation of nonvanishing torsion is a little elusive … Here are some things that are implied by (and are essentially equivalent to) zero torsion:
1) The ability to define the Hessian of a function as a symmetric tensor
2) A parameterized curve is a constant …
- 27.5k
10
votes
Why is it important that partial derivatives commute?
If you don't assume the connection is torsion-free, then there are an infinite number of connections that are compatible with the metric (instead of exactly one), so the link between the geometric properties …
- 27.5k