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How is the Riemann tensor proportinial to the curvature scalar?

  1. Dec 8, 2011 #1
    My professor asks, "Double check a formula that specifies how Riemann tensor is proportional to a curvature scalar." in our homework.

    The closet thing I can find is the relation between the ricci tensor and the curvature scalar in einstein's field equation for empty space.
     
  2. jcsd
  3. Dec 8, 2011 #2
    And by proportinial, I mean proportional.
     
  4. Dec 8, 2011 #3

    haushofer

    User Avatar
    Science Advisor

    He probably means the relation one has for maximally symmetric spaces, which you can find e.g. in Nakahara. It should be something like

    [tex]
    R_{abcd} \propto R [g_{[a[c}g_{d]b]}]
    [/tex]

    You can check this for a sphere, deSitter and antideSitter.
     
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