1. If a surface S, parametrized by X(u.x), has the following coefficients of the first and second fundamental forms, E = (1 + x2)2, F = 0,6 = (1 + u2)2, = 0, f= vituto2, 8= 0, (1) Find the equations in u and v for the lines of curvature. (2) Find the equations in u and v for the asymptotic curves. I have found the principal curvatures: 1 ki = (1 + v2)(1 + u2)/1 + u2 + y2 -1 k2 = (1 + v2)(1 + u2)/1 + u2 + v2 But do not know how to go about these two questions with the information given. Using Differential Geometry of Curves and Surfaces Manfredo P. do Carmo 2nd Edition. This is all the information given to me. 1. If a surface S, parametrized by X(u.x), has the following coefficients of the first and second fundamental forms, E = (1 + x2)2, F = 0,6 = (1 + u2)2, = 0, f= vituto2, 8= 0, (1) Find the equations in u and v for the lines of curvature. (2) Find the equations in u and v for the asymptotic curves. I have found the principal curvatures: 1 ki = (1 + v2)(1 + u2)/1 + u2 + y2 -1 k2 = (1 + v2)(1 + u2)/1 + u2 + v2 But do not know how to go about these two questions with the information given. Using Differential Geometry of Curves and Surfaces Manfredo P. do Carmo 2nd Edition. This is all the information given to me