In polar coordinates, calculate the Riemann curvature tensor of the sphere of unit radius, whose metric is

Question:

In polar coordinates, calculate the Riemann curvature tensor of the sphere of unit radius, whose metric is given in Exer. 28. (Note that in two dimensions there is only one independent component, by the same arguments as in Exer. 18(b). So calculate Rθφθφ and obtain all other components in terms of it.)