Duals of curves in Hyperbolic space

We define two kinds of duals of a curve in Hyperbolic space and investigate the singularities and the relationship from the view point of Legendrian dualities.我们定义了双曲空间（Hyperbolic space）中曲线的两类对偶对象，并从勒让德对偶性（Legendrian dualities）的视角出发，研究其奇点及相互关系。