Something wrong with this do carmo exercise (1.3.3)?

Question

I think I have found an unreported errata to this problem.

Here is my attempt to solve the problem.

Differential Geometry of Curves and Surfaces - Chapter 1 Section 3 Exercise 3

And here is the errata I can found online.

In particular, I believe the errata should include $ \alpha'(t) = (0, 2a) $ when $ t \to \pm \infty $, not $ \alpha'(t) = (2a, 0) $

Can anyone confirm my finding? What should I do to get this included in the errata?

Anyone, please? It is an easy 50 points of reputation just to confirm I am correct. — Andrew Au, Mar 13 '16 at 01:04

score 3 · Accepted Answer · answered Mar 13 '16 at 17:57

3

I am sure I am correct, not sure why there is nobody coming and confirm.

answered Mar 13 '16 at 17:57

Andrew Au

1,127

Thank you for downvoting. Did you find my mistake? – Andrew Au Mar 13 '16 at 19:26
:( The downvote was rather meaningless without a constructive comment. – Andrew Au Mar 13 '16 at 21:21

score 1 · Answer 2 · answered Sep 26 '17 at 13:19

I worked through this and I don't see any mistake. However, that errata is not even close to being complete. For example, page 26 #16 is wrong without assuming an initial curvature/torsion, and page 47 #6(c) should say $\kappa_\beta=\kappa_\alpha/(1+r\kappa_\alpha).$

Something wrong with this do carmo exercise (1.3.3)?

2 Answers2