I ned answer with explanation for this advance math quest

Let H2 : {(m, y) E R2, y 2*: U} be the upper halfplane in R2 and let H 2 have the Riemannian metric 9 such that may) = tiy) fer (my) 6 H2. where (3:, y) is the usual inner product on R2. (a) Compute the components of the LeviCivita connection (i.e., the lChristoi'fel symbols). (13] Let V() = (0,1) be a tangent vector at the point (0,1) IE H2. Let V(t) = (obi), b(t)) be the parallel transport of V(0) along the curve :1: z t, y = 1. Show that VIE) makes an angle t with the direction of the yaxis in the clockwise direction- Consider the hyperboloid S of one sheet x2 + y2 - z2 = 4. (a) Define the Gauss curvature K of S. (b) Use the definition from part (a) to compute K at (0, 2, 0)