HW #5

1. Do Exercise 2 in notes on differential geometry. (This corresponds to Exercise 3.14 on page 108 of the textbook.)
2. Do Exercise 3 in notes on differential geometry. (This corresponds to Exercise 3.15 on page 109 of the textbook.)
3. Derive the equations (8) in notes on differential geometry. (This corresponds to the material of Section 3.2 of the textbook.)
4. Do Exercise 4 in notes on differential geometry.
5. The torus in the figure below is colored green and yellow in the parts where the Gaussian curvature is negative and positive, respectively. Produce a similar graphics.