Conformal vector field

A conformal vector field (often conformal Killing vector field and occasionally conformal or conformal collineation) of a Riemannian manifold (M,g) is a vector field X that satisfies:

$\mathcal{L}_X g=\varphi g$

for some smooth real-valued function φ on M, where $\mathcal{L}_X g$ denotes the Lie derivative of the metric g with respect to X. In the case that φ is identically zero, X is called a Killing vector field.

See also

• Affine vector field
• Curvature collineation
• Homothetic vector field
• Killing vector field
• Matter collineation
• Spacetime symmetries