Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Symmetry (killing vector) preserving diffeomorphisms
  1. Killing vector fields (Replies: 3)

  2. Killing vector help (Replies: 0)

Loading...