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 when the initial data is a ruled surface by straight lines. We give a family of those solutions which are generated by (the isometries of 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 . 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}
}