| Autor: |
Leandro, Benedito, Cintra, Adriana Araujo, Reis, Hiuri Fellipe dos Santos |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Differential Geometry and its Applications 2020 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.difgeo.2020.101633 |
| Popis: |
The aim of this paper is to investigate the mean curvature flow soliton solutions on the Heisenberg group $\mathcal{H}$ when the initial data is a ruled surface by straight lines. We give a family of those solutions which are generated by $\mathfrak{Iso}_{0}(\mathcal{H})$ (the isometries of $\mathcal{H}$ for which the origin is a fix point). We conclude that the function which describe the motion of these surfaces under MCF, is always a linear affine function. As an application we proof that the Grim Reaper solution evolves from a ruled surface in $\mathcal{H}$. We also provide other examples. |
| Databáze: |
arXiv |
| Externí odkaz: |
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