Recurrent tensor: Difference between revisions

Revision as of 01:12, 30 November 2010

Revision as of 14:31, 1 December 2010

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and its property to be torsion-free.

Parallel vector fields (<math>\nabla X = 0</math>) are examples of recurrent tensors that find importance in mathematical research. For example, if <math> X </math> is a recurrent non-null vector field on a [[pseudo-Riemannian manifold]] satisfying

:<math>\nabla X = \omega\otimes X </math>

for some closed [[one-form]] <math> \omega </math>, then X can be rescaled to a parallel vector field <ref>Alekseevsky, Baum (2008)</ref>. In particular, non-parallel recurrent vector fields are lightlikenull vector fields.

===Metric space===