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Relation between affine parameters

  1. Nov 10, 2011 #1
    In Euclidean three-space with coordinates [itex](x,y,z)[/itex] and line element

    [tex]ds^2 = dx^2+dy^2-dz^2[/tex]

    It is easy to show using the geodesic equation that:

    [itex]x = lu+l'[/itex], [itex]y=mu+m'[/itex], [itex]z=nu+n'[/itex]

    where [itex]u[/itex] is an affine parameter.

    However, is it possible to find a relation between [itex]l,m,n[/itex]?
    Last edited: Nov 10, 2011
  2. jcsd
  3. Nov 10, 2011 #2


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    Shouldn't l,m, and n be analogous to a four-velocity in Minowskian space, and hence have a constant norm?
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