3. The four-dimensional fourth-rank Riemann-Christoffel curvature tensor of general rel- ativity, Riklm, satisfies the symmetry relations Riklm = − Rikml = − Rkilm· With the indices running from 0 to 3, show that the number of independent components is reduced from 256 to 36 and that the condition Riklm = Rlmik further reduces the number of independent components to 21. Finally, if the components satisfy an identity Riklm + Rilmk + Rimk! = 0, show that the number of independent components is reduced to 20. Note. The final three-term identity furnishes new information only if all four indices are different. Then it reduces the number of independent components by one-third.