Curves in \(\mathbb {R}^3\)

For a closed curve \(\gamma \colon [a,b]\to \mathbb {R}^3\) with unit tangent field T, we can use a parallel normal vector field to transport a normal vector \(W_a\in T(a)^\perp \) at the starting point of \(\gamma \) to a normal vector \(W_b\in T(b)^\perp \) at the end point.