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

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