Consider the surface patch (u, v) = (cosh u cos v, cosh u sin v, u).

(a) (7 marks) Calculate the Christoffel symbols;

(b) (4 marks) Use the results of (a) to write the geodesic equations for this surface.

(c) (5 marks) Let be the intersection of this surface with the plane z = 1. Let v(t) = (t)u + (t)v be a tangent vector field along . Find a system of two first-order ODE involving and that is equivalent to v being parallel along .

5. Consider the surface patch o (u, v) = (cosh u cos v, cosh u sin v, u). (a) Calculate the Christoffel symbols; (b ) Use the results of (a) to write the geodesic equations for this surface. (c) Let y be the intersection of this surface with the plane z = 1. Let v(t) = a(t)ou + B(t), be a tangent vector field along y. Find a system of two first-order ODE involving o and S that is equivalent to v being parallel along y. (d) Now let y be the intersection of the surface and the XY-plane. Explain how one can solve problem 5 (c) for this curve y without using any information about the Christoffel symbols