- Thread starter
- Banned
- #1

let y:R^3->R^2 unit speed curve of nonvanishing curvature and let its scalar curvature,torsion and Frenet frame be denoted κ, τ and [u,n,b] respectively. You may aassume the frenet formulae are true.

Let M(s,t)=y(s) +tb(s).

1)

Partial derivatives are y'(s)+tb'(s) and b(s). I have to show the cross product is zero.

I get that it's equal to b x (u-τn). I think this is probably non zero but the next question is 2)show that the unit normal vector field is

N(s,t)= $-\frac{n+tτu}{(1+t^{2}τ^{2})^{0.5}}$, which I cannot derive.

Let M(s,t)=y(s) +tb(s).

1)

__Show that M is regular surface.__Partial derivatives are y'(s)+tb'(s) and b(s). I have to show the cross product is zero.

I get that it's equal to b x (u-τn). I think this is probably non zero but the next question is 2)show that the unit normal vector field is

N(s,t)= $-\frac{n+tτu}{(1+t^{2}τ^{2})^{0.5}}$, which I cannot derive.

Last edited: