Study Sections 6.3, 5.1, and 5.2 (through p. 159, Example 2.1) and solve the following problems.
Section 6.3: 2
Section 5.1: 2, 3, 6 (The "if" part only; the "only if" part was on the previous homework), and 8
Section 5.2: 1, 2, 3
1. For a torus, the parallels u=0, u=pi/2, and u = pi are called the maximum parallel, the topmost parallel, and the minimum parallel, respectively. Check which of these parallels are geodesics and which are lines of curvature.
2. Intersect the cylinder x^2 + y^2 =1 with a plane passing through the x axis and making an angle theta with the xy plane. Show that the interscting curve is an ellipse C. Compute the geodesic curvature of C in the cylinder at the points where C meets its axes.