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Lie Groups, Technical/Def.

  1. Nov 17, 2007 #1

    WWGD

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    Hi, everyone:

    I am asked to show that a group G acts by isometries on a space X.

    I am not clear about the languange, does anyone know what this means?.

    Do I need to show that the action preserves distance, i.e, that

    d(x,y)=d(gx,gy)?.

    Thanks.
     
  2. jcsd
  3. Nov 17, 2007 #2
    Depends on context, but if it is a Riemannian manifold, presumably you want to show that the differential of the action preserves the metric tensor.
     
  4. Nov 17, 2007 #3

    WWGD

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    Thanks. I am only told of a linear group, i.e, a group of matrices
    acting on S^3. There is a question on geodesics, so you may
    be right, and we may need to consider this as a Riemannian mfld.
     
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