Meaning of conormal vector

Question

In my situation let $S$ be a surface in $\mathbb{R}^3$ with $\partial S\not=\emptyset$ (enough regular). What is the meaning of $\eta$: conormal vector to $\partial M$ in M? I know it should be normal to $\partial S$ (dimesion 1), so I have a two dimension space for choosing a direction for $\eta$. Thanks in advance.

Answer 1

Conormal vector is different from normal vector of surface. We only talk about conormal vector along the boundary of the surface. Conormal at a boundary point is a vector tangent to the surface but normal to the boundary.