Carnot-Caratheodory and Koranyi-Geodesics in the Heisenberg Group

Carnot-Caratheodory and Koranyi-Geodesics in the Heisenberg Group

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 short...

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Hauptverfasser: Ascher, Josh, Schikorra, Armin
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Classical Analysis and ODEs
Mathematics - Differential Geometry
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Beschreibung
Zusammenfassung: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.
DOI:10.48550/arxiv.2211.04412