Lightlike Dual Surfaces Of Null Curve In De Sitter Space And Legendrian Dual

In this thesis,we investigate the special properties of null curves in de Sitter 3-space,a new Frenet type equation and three important invariants associated with null curves are presented.By means of unfolding theory,the local topological struc-ture of three lightlike dual surfaces is revealed.IL is found that these lightlike dual surfaces have some singularities whose types can be determined by the three invari-ants.Based on the theory of Legendrian dualities on pseudospheres and the theory of contact geometry,it is shown that there exist the ?2,?3,?4-dual relationships between the lightlike transversal curves related to null curves and the three light-like dual surfaces.In addition,an interesting and important fact mentioned in this is that the contact of lightlike transversal curves with lightcone quadrics and the contact of lightlike transversal curves with hyperplanes have the same order at the same type of singularities of three lightlike dual surfaces.