The fundamental theorems for curves and surfaces in 3d Heisenberg group
Differential Geometry
2013-01-29 v1
Abstract
We study the local equivalence problems of curves and surfaces in three dimensional Heisenberg group via Cartans method of moving frames and Lie groups, and find a complete set of invariants for curves and surfaces. For surfaces, in terms of these invariants and their suitable derivatives, we also give a Gaussian curvature fromula of the metric induced from the adapted metric on Heisenberg group, and hence form a new formula for the Euler number of a closed surface.
Keywords
Cite
@article{arxiv.1301.6463,
title = {The fundamental theorems for curves and surfaces in 3d Heisenberg group},
author = {Hung-Lin Chiu and Sin-Hua Lai},
journal= {arXiv preprint arXiv:1301.6463},
year = {2013}
}
Comments
29 pages