1. The problem statement, all variables and given/known data Show that Gij = Gji using the Riemann tensor identity (below) 2. Relevant equations Gij = Rij - 1/2(gijR) Rabcd + Rbcad + Rcabd = 0 R = gmrRmr Rmr = Rmnrn 3. The attempt at a solution I have tried to put the Ricci tensor and Ricci scalar (from the Gij equation) into full Riemann tensor form using the metric. For Gij I get Rij = Rinjn = gnaRinja gijR = gia gjb gab R = gia gjb Rab = gia gjb Ranbn = gia gjb gnd Ranbd So Gij = ( gnaRinja - 1/2 gia gjb gnd Ranbd ) I have done the same for Gji but can't see how to link the two equations using the required Riemann identity. Is this the right approach?