MATH 401 HOMEWORK 1
DUE ON FRIDAY 9-2-05
Complete the following problems (the problems are taken from O’Neill’s Elementary Differential Geometry,
2ed).You are encouraged to work with other students in the class on the problems. You may consult
O’Neill’s book on Elementary Differential Geometry or your lecture notes from class. You may not copy
down the solution if it is in the “Answers to Odd-Numbered Exercises” section of O’Neill. However, once
you complete your solution, you may check your answer to see if you did it “correctly.” You may not
consult the internet or other text books. You must write up your own solutions. Unless the problem is a
computation, please use complete sentences when writing up your solutions. Show your work.
1. 3(f), p. 15
2. 5, p. 15, First convince yourself with some examples or a proof that the identity in Exercise 4 is
true. You may then use this identity to prove Exercise 5.
3. 5, p. 39
4. 8, p. 40
5. 9, p. 40
6. 1, p. 26
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