Suppose that on a Riemannian manifold (M,g) there is a killing vector such that(adsbygoogle = window.adsbygoogle || []).push({});

##\mathcal{L}_{\xi} g = 0.##

How would one then characterize the group of diffeomorphisms ##f: M \to M## such that

$$\mathcal{L}_{f^* \xi} (f^*g) = 0?$$

How would one describe them? Do they have a name and can an explicit form be found?

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# Symmetry (killing vector) preserving diffeomorphisms

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