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arXiv · 1301.6463

The fundamental theorems for curves and surfaces in 3d Heisenberg group

Hung-Lin Chiu·Sin-Hua Lai
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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.

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Hung-Lin Chiu, Sin-Hua Lai. 2013-01-28. The fundamental theorems for curves and surfaces in 3d Heisenberg group. https://arxiv.org/abs/1301.6463

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