## How is the Riemann tensor proportinial to the curvature scalar?

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.
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 And by proportinial, I mean proportional.
 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 $$R_{abcd} \propto R [g_{[a[c}g_{d]b]}]$$ You can check this for a sphere, deSitter and antideSitter.