# A differential geometry question

1. Jan 24, 2010

### binglee

Show that the knowledge of the vector function n = n(s) (normal vector) of a unit-speed
curve
, with non-zero torsion everywhere, determines the curvature and the torsion
don't have any clues about what i am supposed to prove!!~

2. Jan 24, 2010

### owlpride

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.

3. Jan 24, 2010

### binglee

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

4. Jan 24, 2010

### binglee

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??