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Homework Help: Minimal surfaces questions

  1. Oct 19, 2011 #1
    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. jcsd
  3. Oct 19, 2011 #2


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    Science Advisor

    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?
  4. Oct 19, 2011 #3
    Edited the first post for a relevant equation.

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