An affine vector field (sometimes affine collineation or affine) is a projective vector field preserving geodesics and preserving the affine parameter. Mathematically, this is expressed by the following condition:
:<math>(\mathcal{L}_X g_{ab})_{;c}=0
</math>
See also
- Conformal vector field
- Curvature collineation
- Homothetic vector field
- Killing vector field
- Matter collineation
- Spacetime symmetries