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:

$({{ℒ}}_X{g}_{ab}{)}_{;c}=0$

See also

• Conformal vector field
• Curvature collineation
• Homothetic vector field
• Killing vector field
• Matter collineation
• Spacetime symmetries

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