Physics: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:

[math]\displaystyle{ (\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