Carnot-Caratheodory and Koranyi-Geodesics in the Heisenberg Group
Differential Geometry
2022-11-09 v1 Classical Analysis and ODEs
Abstract
This paper is part of an undergraduate research project. We discuss the Heisenberg group H1, the three-dimensional space R3 equipped with one of two equivalent metrics, the Koranyi- and Carnot- Caratheodory metric. We show that the notion of length of curves for both metrics coincide, and that shortest curves, so-called geodesics, exist.
Cite
@article{arxiv.2211.04412,
title = {Carnot-Caratheodory and Koranyi-Geodesics in the Heisenberg Group},
author = {Josh Ascher and Armin Schikorra},
journal= {arXiv preprint arXiv:2211.04412},
year = {2022}
}