A conformal Killing vector field generates a local flow that preserves the metric up to a position-dependent scale factor.
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A **Conformal Killing vector field** is a special type of vector field that characterizes the symmetry properties of a geometric structure in a conformal manner. Specifically, a vector field \( V \) on a Riemannian (or pseudo-Riemannian) manifold is called a conformal Killing vector field if it satisfies a particular condition related to the metric of the manifold.