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Unsymmetrical metric

  1. May 9, 2010 #1
    Could anyone give me an example of two-dimensional metric which
    doesn't have any Killing vector. It's not so easy to prove that
    particular metric is indeed unsymmetrical - it may be only written
    in unfortunately chosen coordinates :).

    Any ideas how to attack this apparently simple problem.
     
  2. jcsd
  3. May 9, 2010 #2

    atyy

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    Science Advisor

    http://arxiv.org/abs/0910.0350

    Section 4 has a spacetime with no Killing vectors, but it's not 2D. Maybe the reference where they show this will help?
     
  4. May 9, 2010 #3

    Nabeshin

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    Indeed hard to prove... Why not just try something absurd?
    [tex]ds^2=e^{2x^2y}\left(dx^2+dy^2\right)+cosh^2\left(x^5\right) dx dy[/tex]
     
  5. May 9, 2010 #4
    Maybe this - matric induced form three dimensional flat euclidan space
    on two dimensional ellipsoid with three unequal sides shouldn't posses any Killing
    vectors. Am I right?
    (none of killing vectors of eucliden space preserves this ellipsoid)
     
  6. May 9, 2010 #5
    Damn, I'm stumped here, but interested.
     
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