A differential geometry question

[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!~

 

[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.

 

[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

 

[binglee]

bump can anybody 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!~~

 

[Bacle]

binglee:

Have you tried working with Frenet-Serre frames.?