Closed Surfaces

Abstract

AbstractWe define a closed surface as a surface $$f\colon M\to \mathbb {R}^3$$ f : M → ℝ 3 whose boundary components have been matched in pairs in such a way that f as well as its unit normal N are continuous across the boundary. This allows us to prove an analog of the fact that the tangent winding number of a closed plane curve is an integer.