On the non-parabolicity of $Sol_3$

Leonardo Bonorino; Giovanni Nunes; Álvaro Ramos; Jaime Ripoll; Lisandra Sauer; Miriam Telichevesky

On the non-parabolicity of $Sol_3$

Differential Geometry 2023-12-29 v1

Authors: Leonardo Bonorino , Giovanni Nunes , Álvaro Ramos , Jaime Ripoll , Lisandra Sauer , Miriam Telichevesky

Abstract

We prove that $Sol_3$ , the isometry group of the Minkowski plane, is non parabolic with respect to any left invariant metric.

Keywords

Sol_3 geometry non-parabolic isometry group Minkowski plane left invariant metric

Cite

@article{arxiv.2312.16302,
  title  = {On the non-parabolicity of $Sol_3$},
  author = {Leonardo Bonorino and Giovanni Nunes and Álvaro Ramos and Jaime Ripoll and Lisandra Sauer and Miriam Telichevesky},
  journal= {arXiv preprint arXiv:2312.16302},
  year   = {2023}
}