Given that $R_{abcd}=-R_{bacd}$, $R_{abcd}=-R_{abdc}$ and $R_{abcd}=R_{cdab}$ can I prove that $R_{abcd}+R_{acdb}+R_{adbc}=0$ without using the definition of the Riemann curvature tensor? Are the above identities sufficient?


closed as off-topic by knzhou, Qmechanic Dec 4 '18 at 14:44

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