# .

# Affine vector field

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:

\( (\mathcal{L}_X g_{ab})_{;c}=0 \)

See also

Conformal vector field

Curvature collineation

Homothetic vector field

Killing vector field

Matter collineation

Spacetime symmetries

Retrieved from "http://en.wikipedia.org/"

All text is available under the terms of the GNU Free Documentation License