Legendrian

Some articles on legendrian:

Legendrian Knot
... In mathematics, a Legendrian knot often refers to a smooth embedding of the circle into, which is tangent to the standard contact structure on ... 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 ... There can be inequivalent Legendrian knots that are isotopic as topological knots ...
Dehn Planes - Dehn's Non-Legendrian Geometry
... In the same paper, Dehn also constructed an example of a non-Legendrian geometry where there are infinitely many lines through a point not meeting ... of any triangle is greater than π The non-Legendrian geometry consists of the points (xy1) of this affine subspace such that tx and ty are finite (where as ...
Contact Geometry - Legendrian Submanifolds and Knots
... The most interesting subspaces of a contact manifold are its Legendrian submanifolds ... Legendrian submanifolds are analogous to Lagrangian submanifolds of symplectic manifolds ... There is a precise relation the lift of a Legendrian submanifold in a symplectization of a contact manifold is a Lagrangian submanifold ...
Relative Contact Homology - Legendrian Knots
... The simplest case yields invariants of Legendrian knots inside contact three-manifolds ... purely combinatorial version of relative contact homology for Legendrian knots, i.e ... a combinatorial invariant for loops of Legendrian knots, with which he detected differences between the fundamental groups of the space of smooth knots ...