I want some one explain to me; this part is not clear to me.
Q: Show that curve $c$ with positive curvature is asymptotic if and only if if its binormal $B$ is parallel to the unit normal of $S$ at all points of $c$
A: Since $K_n=0 \iff$ $c''$ is perpendicular to $N$ $\iff$ $N$ is perpendicular to $n$ $\iff$ $N$ is parallel to $B$ (since $N$ is perpendicular to $T$).
Here, $c''$ is the second derivative, $B$ binormal vector, $K_n$ normal curvature.
My question is
I know from Frenet–Serret formulas that $N$ is perpendicular to $B$ and $N$ is perpendicular to $T$ and $B$ is perpendicular to $T$. In the question it changes, it said that $N$ is parallel to $B$. Why did this change? Can any one explain this part please?
Why is $N$ perpendicular to $n$? Where this come from?
These are my questions, I hope someone can help me to understand please. If possible, draw a figure. Thank you.