How is the Riemann tensor proportinial to the curvature scalar?

Lyalpha

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.

Lyalpha

And by proportinial, I mean proportional.

haushofer

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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Lyalpha	How is the Riemann tensor proportinial to the curvature scalar? Tweet 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.

haushofer Recognitions: 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.