Differential Gemometry

question 17, page 55 Shifrin's book Below is the question : 17 How is the Frenet frame along an asymptotic curve related to the geometry of the surface? Suppose K.P / < 0. If C is an asymptotic curve with .P / ¤ 0, prove that its torsion satisfies p j.P /j D K.P /. (Hint: If we choose an orthonormal basis fU; Vg for T P .M / with U tangent to C , what is the matrix for S P ? See the Remark on p. 47.) Note : please check the file also in order to solve the question .