Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898355 | Differential Geometry and its Applications | 2018 | 12 Pages |
Abstract
We study the horizontally regular curves in the Heisenberg groups Hn. We prove a fundamental theorem for curves in Hn(nâ¥1) and define the order of horizontally regular curves. We also show that the curve γ is of order k if and only if, up to a Heisenberg rigid motion, γ lies in Hk but not in Hkâ1; moreover, two curves with the same order differ in a rigid motion if and only if they have the same invariants: p-curvatures and contact normality. Thus, combining these results with our previous work [3] we get a complete classification of horizontally regular curves in Hn for nâ¥1.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hung-Lin Chiu, XiuHong Feng, Yen-Chang Huang,