# Legendrian knot

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