Conformal vector field
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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