Ionic radius: Difference between revisions

Revision as of 18:59, 13 January 2014

A curvature collineation (often abbreviated to CC) is vector field which preserves the Riemann tensor in the sense that,

ℒ_{X} R^{a}_{b c d} = 0

where $R^{a}_{b c d}$ are the components of the Riemann tensor. The set of all 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 $C C (M)$ and may be infinite-dimensional. Every affine vector field is a curvature collineation.

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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]]

Ionic radius: Difference between revisions

Revision as of 18:59, 13 January 2014

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