Math205c Spring Term 2003

Assignment 22

1. Find a parametric representation for a “circular doughnut”.

2. Give concrete examples for all possible ways an immersion can fail to be an embedding.

3. Let M_{m} ⊂ ℝ^{n} be an m-dimensional C^{1}-manifold. Show that the tangent space to M_{m} at any point x ∈ M_{m} does not depend on the choice of local representation g for the manifold.

4. Consider an ideal point on a wheel of radius R located at distance r ≤ R from its center. Parametrize the curve traced by this point as the wheel is rolling along a horizontal line.

5. You ask a question.

The Homework is due Friday, May 16.