Solution
= Solution
$R_{\mu\nu\alpha\beta}=-R_{\nu\mu\alpha\beta}=-R_{\mu\nu\beta\alpha}=R_{\alpha\beta\mu\nu}$ and $R_{\mu[\nu\alpha\beta]}=0$. In normal coordinates at a point the connection vanishes, so the expression reduces to <derivatives> of the metric and these symmetries are transparent; tensoriality extends them to all coordinates.