Difference between revisions of "Torsion is antisymmetric"
(Created page with "==Statement== Let <math>M</math> be a differential manifold and <math>\nabla</math> be a fact about::linear connection on <math>M</math> (viz., <math>\nabla</math> is...")
Latest revision as of 17:51, 6 January 2012
Consider the torsion of , namely:
Then, is antisymmetric, i.e.:
Equivalently, is alternating, i.e.:
The proof follows directly from the definition, and the fact that the Lie bracket of derivations is antisymmetric.