The Robertson-Walker geometry (to be discussed in Chapter 9) has a spacetime interval ds = dt-a(t) [dx + sin x (do+ sin0do)] where the coordinates are x = t, x = x, x = 0, x = 0, and a(t) is a function of time. (a) Calculate all the Christoffel symbols Im with purely spatial indices; that is, with indices from 1 to 3. (b) A covariant vector with components b = (0, 1, 0, 0) is initially located at X = Xo in the equatorial plane 0 = /2. We parallel-transport this vector instantaneously (dt = 0) once around a closed circle in the equatorial plane (x = Xo, 0 = /2, p = 0 to 27). Calculate the final vector bu that results from this parallel transport.