MATH 4250/6250 Problem Set 6, February 13, 2009

Don't hand in.

Compute the metric tensor (g_{i j}) for the surfaces in problem sets 4 and 5.

As explained in class today, if x(u,v) is a coordinate patch, then g_{i j} is the dot product of x_i and x_j , where x₁ = x_uand x₂ = x_v.

4A(a) Saddle surface

4A(b) Surfaces of revolution

4A(c) Torus

4A(d) Moebius strip

5.1 Ruled surfaces

5.3 Stereographic coordinates on the sphere