English

A family of MCF solutions for the Heisenberg Group

Differential Geometry 2021-11-02 v1

Abstract

The aim of this paper is to investigate the mean curvature flow soliton solutions on the Heisenberg group H\mathcal{H} when the initial data is a ruled surface by straight lines. We give a family of those solutions which are generated by Iso0(H)\mathfrak{Iso}_{0}(\mathcal{H}) (the isometries of H\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 H\mathcal{H}. We also provide other examples.

Keywords

Cite

@article{arxiv.1904.12015,
  title  = {A family of MCF solutions for the Heisenberg Group},
  author = {Benedito Leandro and Adriana Araujo Cintra and Hiuri Fellipe dos Santos Reis},
  journal= {arXiv preprint arXiv:1904.12015},
  year   = {2021}
}