Torsion tensor

Manner of characterizing a twist or screw of a moving frame around a curve

In differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is bilinear map of two input vectors , that produces an output vector representing the displacement within a tangent space when the tangent space is developed along an infinitesimal parallelogram whose sides are . It is skew symmetric in its inputs, because developing over the parallelogram in the opposite sense produces the opposite displacement, similarly to how a screw moves in opposite ways when it is twisted in two directions.

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