Torsion tensor
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Revision as of 11:50, 15 March 2013
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1 Definition
Let be a smooth manifold and a covariant derivative on . Then the expression ,
(1)
for all vector fields is a tensor, called torsion tensor. A covariant derivative is called torsion free if . In terms of coordinates, using a local parametrization , the vanishing of the torsion means
(2)
for any where .