Recurrent tensor: Difference between revisions

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In mathematics, a '''recurrent tensor''' with respect to a [[connection (mathematics)|connection]] <math>\nabla</math> on a [[manifold]] ''M'' is a [[tensor]] ''T'' for which there is a [[differential form|one-form]] ''&omega;'' on ''M'' such that

==definition==

Let <math>\nabla</math> be a connection on a manifold ''M''. A tensor ''T'' called '''recurrent with respect to <math>\nabla</math>''', iff there is a one-form <math>\omega</math> on ''M'', such that

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

==exampleExample==

An example for a recurrent tensor is a [[Weyl structure]] on &nbsp;''M''.