a. Prove that a is a line of curvature in M if and only if (noa)'(t) = k(t)a'(t), where k(t) is the principal curvature at a(t) in the direction a' (t). (More colloquially, differentiating along the curve a, we just write 11' = ka'.) Suppose two surfaces M and M * intersect along a curve C . Suppose C is a line of curvature in M . Prove that C is a line of curvature in M * if and only if the angle between M and M * is constant along C. (In the proof of