Legendrian knot

In mathematics, a Legendrian knot often refers to a smooth embedding of the circle into ${\displaystyle \mathbb {R} ^{3}}$, which is tangent to the standard contact structure on ${\displaystyle \mathbb {R} ^{3}}$. It is the lowest-dimensional case of a Legendrian submanifold, which is an embedding of a k-dimensional manifold into a (2k+1)-dimensional contact manifold that is always tangent to the contact hyperplane.