I got trouble to understand the cyclic sum identity (the first Bianchi identity) of the Riemann curvature tensor:
{R^\alpha}_{[ \beta \gamma \delta ]}=0
or equivalently,
{R^\alpha}_{\beta \gamma \delta}+{R^\alpha}_{\gamma \delta \beta}+{R^\alpha}_{\delta \beta \gamma}=0.
I can understand the...