ABSTRACT
The theory of Legendrian knots first introduced by Dmitry Fuchs and Serge Tabachnikov, lies at the juncture of knot theory, the theory of wave fronts and contact geometry. The Legendrian knot theory is interesting because it allows introducing a new equivalence for knots: besides topological isotopy, one can consider a more subtle isotopy in the space of Legendrian knots. One of the main questions of the theory of differential equations is to find an enveloping curve for the family of straight lines on the plane. It is well known that in the smooth case, this problem has a solution according to the existence and uniqueness theorem. Legendrian knots and links in their frontal projection admit a combinatorial interpretation like ordinary knots and links. Namely, there exists a set of elementary moves transforming one frontal projection of a Legendrian link to each other projection of the same link.
