The subject is differential geometry, and I'm using this question to help me understand how to solve problems in the book reference is Differential geometry Theodore shifrin university of Georgia Please solve thoroughly and explain details from Rob sent you thumbs up. Thank you.

11. (The Bishop Frame) Suppose or is an arclength-parametrizationpose we have @ unit vector fields N1 and N2 = T x Nj along a so that T . N1 = T . N2 = N1 . N2 = 0; i.e., T, N1, N2 will be a smoothly varying right-handed orthonormal frame as we move along the curve. (To this point, the Frenet frame would work just fine if the curve were C' with k # 0.) But now we want to impose the extra condition that N', . N2 = 0. We say the unit normal vector field N1 is parallel along a; this means that the only change of N1 is in the direction of T. In this event, T, N1, N2 is called a Bishop frame for a. A Bishop frame can be defined even when a Frenet frame cannot (e.g., when there are points with