Affine vector field

{{Short description|Type of vector field}} {{Multiple issues| {{unreferenced|date=February 2018}} {{context|date=February 2018}} {{technical|date=July 2025}} }}

An '''affine vector field''' (sometimes '''affine collineation''' or '''affine''') is a [[projective vector field]] preserving [[geodesic]]s and preserving the [[affine parameter]]. Mathematically, this is expressed by the following condition:

:<math>(\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]]

[[Category:Mathematics of general relativity]]

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