Is there any particular reason that scalar curvature is defined [tex] R = g^{ab}R_{ab} [/tex] instead of [tex] R = R^{ab}R_{ab} [/tex] ?(adsbygoogle = window.adsbygoogle || []).push({});

Do both scalars share the property that they are zero if and only if every component of [itex] R^{a}_{bcd} [/itex] is also zero?

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# About scalar curvature

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