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Riemann tensor in 3 dimension

  1. Jun 24, 2013 #1

    Riemann tensor has a definition that independent of coordinate and dimension of manifold where you work with it.

    see for example Geometry,Topology and physics By Nakahara Ch.7
    In that book you can see a relation for Riemann tensor and that is usual relation according to Christoffel symbol and it's derivative. ( that relation is independent of dimension of manifold)
    I don't know why Riemann tensor in 3D has the following form


    In this page
    you can see a prove for 3D Riemann tensor but i can't understand why it has different form
  2. jcsd
  3. Jun 24, 2013 #2


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    Post #7 in that thread has the exact same form of the equation in your attachment. The only difference is samalkhaiat pulled out a negative sign in the Ricci scalar term in the final expression.
    Last edited: Jun 24, 2013
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