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A differential geometry question

  1. Jan 24, 2010 #1
    Show that the knowledge of the vector function n = n(s) (normal vector) of a unit-speed
    , with non-zero torsion everywhere, determines the curvature and the torsion
    don't have any clues about what i am supposed to prove!!~
  2. jcsd
  3. Jan 24, 2010 #2
    You are supposed to compute the curvature and torsion of a curve from its normal vector function. You probably defined curvature and torsion as a function of the tangent vector.
  4. Jan 24, 2010 #3
    ya, we defined curvature = ||r''||=||t'||. It is a function of t, while we defined torsion = -n.b' it is not a function of t. I don't know if my understanding about torsion is right. Since we defined n as a function of t and b as a function of t so is t. Then in this question i just need to go through the same process wrt n??right? thank you for your helping
  5. Jan 24, 2010 #4
    bump can any body help me???!!~~~~
    I thought about it for a while. what does it mean by the knowledge of n?
    if we know t n b, we can determine the curvature and the torsion, but here we only know n??
    please!!~ help me!!~~
  6. Jan 26, 2010 #5

    Have you tried working with Frenet-Serre frames.?
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