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Symmetry (killing vector) preserving diffeomorphisms

  1. Feb 4, 2014 #1
    Suppose that on a Riemannian manifold (M,g) there is a killing vector such that
    ##\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?
     
  2. jcsd
  3. Feb 6, 2014 #2
    Alternatively, given a killing vector ##\xi## how would one describe the diffeomorphisms ##f: M \to M## such that ##\xi## remains a killing vector also for ##f^* g##? I.e. ##\mathcal{L}_{\xi} f^*g = 0##.
     
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