DR-DP-Matrix: Difference between revisions
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A '''conformal vector field''' (often '''conformal Killing vector field''' and occasionally '''conformal''' or '''conformal collineation''') of a [[Riemannian manifold]] <math>(M,g)</math> is a [[vector field]] <math>X</math> that satisfies: | |||
< | :<math>\mathcal{L}_X g=\varphi g</math> | ||
< | |||
for some smooth real-valued function <math>\varphi</math> on <math>M</math>, where <math>\mathcal{L}_X g</math> denotes the [[Lie derivative]] of the metric <math>g</math> with respect to <math>X</math>. In the case that <math>\varphi</math> is identically zero, <math>X</math> is called a [[Killing vector field]]. | |||
< | ==See also== | ||
< | |||
* [[Affine vector field]] | |||
* [[Curvature collineation]] | |||
* [[Homothetic vector field]] | |||
* [[Killing vector field]] | |||
* [[Matter collineation]] | |||
* [[Spacetime symmetries]] | |||
{{relativity-stub}} | |||
[[Category:Mathematical methods in general relativity]] | |||
Latest revision as of 10:37, 6 December 2013
A conformal vector field (often conformal Killing vector field and occasionally conformal or conformal collineation) of a Riemannian manifold is a vector field that satisfies:
for some smooth real-valued function on , where denotes the Lie derivative of the metric with respect to . In the case that is identically zero, is called a Killing vector field.
See also
- Affine vector field
- Curvature collineation
- Homothetic vector field
- Killing vector field
- Matter collineation
- Spacetime symmetries
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