Math 442 Differential Geometry Winter 2003
Assignment #6: Due Wednesday, 2/19/03
Remark: As I mentioned in class, do Carmo consistently fails to distinguish between what I call
the tangent plane and the affine tangent plane. So in each of the problems below, part of your job
is to decide which of these concepts do Carmo means when he says “tangent plane.” Be sure to
indicate which interpretation you’re choosing.
I. Reading:
•Read do Carmo, Section 2-4 (pages 83–88).
II. Practice problems:
1. do Carmo, Section 2-4 (pp. 88–92), #1, 2, 3, 11.
III. Required problems:
1. do Carmo, Section 2-4 (pp. 88–92), #5.
2. do Carmo, Section 2-4 (pp. 88–92), #7.
3. do Carmo, Section 2-4 (pp. 88–92), #8.
4. do Carmo, Section 2-4 (pp. 88–92), #13.
5. do Carmo, Section 2-4 (pp. 88–92), #18.
6. do Carmo, Section 2-4 (pp. 88–92), #21.
7. do Carmo, Section 2-4 (pp. 88–92), #26.