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 Fáry–Milnor type theorem, together with Bray–Jauregui type theorem. We also prove the fundamental theorem of curves in the standard CR 3-sphere S 3 . As an application, we classify some horizontally regular curves in S 3 .