2022/11/08 by Josh Ascher, Armin Schikorra, Ascher, Josh +1
Mathematics · Engineering · #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #3D Shape Modeling and Analysis
paper · pdf · doi:10.48550/arxiv.2211.04412
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.