In mathematics, a Legendrian knot often refers to a smooth embedding of the circle into R 3 {\displaystyle \mathbb {R} ^{3}} , which is tangent to the standard contact structure on R 3 {\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.
In mathematics, a Legendrian knot often refers to a smooth embedding of the circle into R 3 {\displaystyle \mathbb {R} ^{3}} , which is tangent to the standard contact structure on R 3 {\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.
Source: Wikipedia "Legendrian knot" · CC BY-SA 4.0
Share this article: X · Bluesky