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Ricci scalar computation quick question

  1. Jan 3, 2015 #1
    1. The problem statement, all variables and given/known data

    I am trying to compute ##R## from the 3-d metric: ##ds^{2}=d\chi^{2}+f^{2}\chi(d\theta^{2}+sin^{2}\theta d\phi^{2})##


    2. Relevant equations

    The space also satisfies the below relationships:
    ##R=3k##
    ## R_{abcd}=\frac{1}{6}R(g_{ac}g_{db}-g_{ad}g_{bc})## [1]

    3. The attempt at a solution

    I think I need to compute the christoffel symbols, then the Riemann tensor, and contract etc.
    I'm just wondering whether the task is meant to be simplified by eq [1]?( I can see the metric is diagonal and so this reduces the number of non-zero christoffel symobols...)

    Thanks in advance.
     
    Last edited by a moderator: Jan 3, 2015
  2. jcsd
  3. Jan 4, 2015 #2

    Matterwave

    User Avatar
    Science Advisor
    Gold Member

    What is "k" in equation 1?
     
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