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Riemann metric

  1. Dec 22, 2009 #1
    Find the Riemann tensor of the 2-sphere of radius r

    S[tex]^{2}_{r}[/tex]={(x,y,z) [tex]\in[/tex][tex]\Re^{3}[/tex]|x[tex]^{2}[/tex] + y[tex]^{2}[/tex] + z[tex]^{2}[/tex] = r[tex]^{2}[/tex]}

    with metric g obtained as the pull-back of the Euclidean metric gR3 by the inclusion
    map S[tex]^{2}[/tex] [tex]\hookrightarrow[/tex][tex]\Re^{3}[/tex].

    Any help would be appreciated. Thanks
  2. jcsd
  3. Dec 22, 2009 #2


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    This seems to be a pretty straight forward problem. Rewrite your metric in spherical coordinates. Identify your [itex] g_{\mu \nu} [/itex]. Go to a book on General Relativity and find the definition of the Riemann tensor in terms of the Christoffel symbols and calculate it out. It will take a little time, but it's not hard.
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