Difference between revisions of "Torsion of a linear connection"
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Revision as of 20:12, 18 May 2008
This article defines a tensor (viz a section on a tensor bundle over the manifold) of type (1,2)
Definition
Given data
 A differential manifold
 A linear connection on (viz., a connection on the tangent bundle ).
Definition part
The torsion of , denoted as , is defined as a map that takes as input 2 vector fields and outputs a third vector field, as follows:
A linear connection whose torsion is zero is termed a torsionfree linear connection.
Tensoriality
Further information: Torsion is tensorial The torsion map is a tensor. It is tensorial in both and .