Carnot-Carathéodory and Korányi-Geodesics in the Heisenberg Group

Mathematics Exchange 2026 Open access

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Authors: Josh Ascher, Armin Schikorra
DOI: 10.33043/3dem6hfd3v
Cited by: 0

Abstract

We discuss the Heisenberg group H1, the three-dimensional space R^3 equipped with one of two equivalent metrics, the Korányi- and Carnot-Carathéodory metric. We show that the notion of length of curves for both metrics coincide, and that shortest curves, so-called geodesics, exist.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Advanced Differential Geometry Research Geometry and complex manifolds

Publication details

Journal / source
Mathematics Exchange
Volume
16
Issue
1
Pages
85–103
Publication date
3 March 2026
Language
EN