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arXiv · 1605.05076

Ruled surfaces of finite type in 3-dimensional Heisenberg group

Mohammed Bekkar
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Abstract

In this paper, on the first, we prove $Δr=2H$ where $Δ$ is the Laplacian operator, $r=\left( r_{1},r_{2},r_{3}\right) $ the position vector field and $H$ is the mean curvature vector field of a surface $\mathcal{S}$ in the 3-dimensional Heisenberg group $H_{3}.$ In the second, we classify the ruled surfaces by straight geodesic lines, which are of finite type in $H_{3}.$ The straight geodesic lines belong to $\ker ω,$ where $ω$ is the Darboux form.

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Mohammed Bekkar. 2016-05-17. Ruled surfaces of finite type in 3-dimensional Heisenberg group. https://arxiv.org/abs/1605.05076

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