Conformal Killing vector field

In conformal geometry, a conformal Killing vector field on a manifold of dimension n with (pseudo) Riemannian metric g {\displaystyle g} (also called a conformal Killing vector, CKV, or conformal colineation), is a vector field X {\displaystyle X} whose (locally defined) flow defines conformal transformations, that is, preserve g {\displaystyle g} up to scale and preserve the conformal structure. Several equivalent formulations, called the conformal Killing equation, exist in terms of the Lie derivative of the flow e.g.

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