Help Hints to do the question 1. Focus on N dot U = cos (theta) where N is the normal vector of the curve in R^3 and U is the unit normal of the sphere. When you have an equation like this, what must you do? Newton would do it. And, on the right, what rule do you have to use when you take a derivative with respect to s, not theta? 2. What is special about U' for the sphere? We know the shape operator for the sphere. 3. What vectors is T perpendicular to: N, B, U? What does this mean about these three vectors? Draw a picture and use what you know about the angle between N and U. 4. What does this tell you about tau, the torsion? 5. Remember, a smooth closed curve means that alpha (a) =alpha (b) and alpha'(a) =alpha'(b). So why does the integral of tau from a to b equal zero??? Really think about the hint. Please answer the question with correct solution, CLEAR explanation and CLEAR steps... will send lectures please see that and book online ( Differential Geometry and Its Applications) THANK YOU