Global Differential Geometry of Curves in Three-Dimensional Heisenberg Group and CR Sphere

摘要

In this paper, we study some global properties of curves in the Heisenberg group H-1. In particular, we obtain Fenchel-type theorem and Fary-Milnor type theorem, together with Bray-Jauregui type theorem. We also prove the fundamental theorem of curves in the standard CR3-sphere S-3. As an application, we classify some horizontally regular curves in S-3.