Ionic radius: Difference between revisions

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A '''curvature collineation''' (often abbreviated to '''CC''') is [[vector field]] which preserves the [[Riemann tensor]] in the sense that,
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:<math>\mathcal{L}_X R^a{}_{bcd}=0</math>
 
where <math>R^a{}_{bcd}</math> are the components of the Riemann tensor. The [[Set (mathematics)|set]] of all [[smooth function|smooth]] curvature collineations forms a [[Lie algebra]] under the [[Lie bracket]] operation (if the smoothness condition is dropped, the set of all curvature collineations need not form a Lie algebra). The Lie algebra is denoted by <math>CC(M)</math> and may be [[infinity|infinite]]-[[dimension]]al. Every [[affine vector field]] is a curvature collineation.
 
==See also==
 
* [[Conformal vector field]]
* [[Homothetic vector field]]
* [[Killing vector field]]
* [[Matter collineation]]
* [[Spacetime symmetries]]
 
{{relativity-stub}}
 
[[Category:Mathematical methods in general relativity]]

Latest revision as of 13:23, 7 January 2015

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