Homework Help: Minimal surfaces questions

1. Oct 19, 2011

Applejacks

1. The problem statement, all variables and given/known data

Prove that there are no tubes that are minimal surfaces

2. Relevant equations
F(u, v) = γ(u) + R(cosuN(v) + sinuB(v))

3. The attempt at a solution

A tube is defined to be the surface formed by drawing circles with constant radius in the normal plane in a space curve.

I know that a minimal surface is a surface with a mean curvature of zero. So to prove the tubes aren't minimal surfaces, I need to show that the mean curvature is non-zero. I just don't know what the first step to take here is. Any tips/suggestions?

Last edited: Oct 19, 2011
2. Oct 19, 2011

HallsofIvy

Assume the curve is given by the parametric equation x= f(t), y= g(t), z= h(t). Can you write parametric equations for a point on the tube?

3. Oct 19, 2011

Applejacks

Edited the first post for a relevant equation.

Wouldn't x=rcost, y=rsint and z=t?