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?