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arXiv · 2211.04412

Carnot-Caratheodory and Koranyi-Geodesics in the Heisenberg Group

Josh Ascher·Armin Schikorra
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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.

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Josh Ascher, Armin Schikorra. 2022-11-08. Carnot-Caratheodory and Koranyi-Geodesics in the Heisenberg Group. https://arxiv.org/abs/2211.04412

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