# Affine vector field

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Type of vector field

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An **affine vector field** (sometimes **affine collineation** or **affine**) is a [projective vector field](/source/Projective_vector_field) preserving [geodesics](/source/Geodesic) and preserving the [affine parameter](/source/Affine_parameter). Mathematically, this is expressed by the following condition:

- ( L X g a b ) ; c = 0 {\displaystyle ({\mathcal {L}}_{X}g_{ab})_{;c}=0}

## See also

- [Conformal vector field](/source/Conformal_vector_field)

- [Curvature collineation](/source/Curvature_collineation)

- [Homothetic vector field](/source/Homothetic_vector_field)

- [Killing vector field](/source/Killing_vector_field)

- [Matter collineation](/source/Matter_collineation)

- [Spacetime symmetries](/source/Spacetime_symmetries)

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