Extended Legendrian Dualities Theorem in Singularity Theory

Abstract

In this paper, we find some new information on Legendrian dualities and extend them to the case of Legendrian dualities for continuous families of pseudo-spheres in general semi-Euclidean space. In particular, we construct all contact diffeomorphic mappings between the contact manifolds and display them in a table that contains all information about Legendrian dualities.

Keywords

• Legendrian dualities
• Legendrian singularity theory
• semi-Euclidean space