For reference, the definitions of the Christoffel symbol, the Riemann Christoffel curvature tensor, the Ricci curvature tensor, and the scalar curvature tensor are given in order as follows:
(1) Γng = dEP
(2) Rpg = dEP
(3) Rvp = RVp
(4) R = g"PRvp
Using these definitions, calculate all three curvature tensors for the 2-d space of the surface of a sphere. For reference, the labeling vector for a spherical surface is: R = iRsinθcosφ + iRsinθsinφ + iRcosθ. The two coordinates of interest are θ and φ. The symbol R is the radius of the sphere and the symbol i = ±1. Also, based on your calculation, is the curvature of a sphere positive or negative?