Curves in $$\mathbb {R}^3$$

Abstract

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