Local Conformal Transformations:Coordinate or metric transformations?

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Johanna222
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Hello,

I'm wondering what the exact definition of a local conformal transformation is, in the context of General Relativity (/Shape Dynamics)

To be more precise:
1. Are local conformal transformations coordinate transformations or scalar transformations of the metric?
2. If they are coordinate transformations, are they of the form [itex]\vec{x} \mapsto C(x^{\mu})\vec{x}[/itex], with [itex]C(x^{\mu})[/itex] a differentiable function?

Good evening to you all!
 
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