Physics: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:

${{ℒ}}_{X}g=\phi g$

for some smooth real-valued function $\phi$ on $M$, where ${{ℒ}}_{X}g$ denotes the Lie derivative of the metric $g$ with respect to $X$. In the case that $\phi$ 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