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Minimal surfaces questions

  • Thread starter Applejacks
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  • #1
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Homework Statement



Prove that there are no tubes that are minimal surfaces

Homework Equations


F(u, v) = γ(u) + R(cosuN(v) + sinuB(v))


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:

Answers and Replies

  • #2
HallsofIvy
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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
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Edited the first post for a relevant equation.

Wouldn't x=rcost, y=rsint and z=t?
 

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