论文标题
Heisenberg Group中的Carnot-Caratheodory和Koranyi-Geodesics
Carnot-Caratheodory and Koranyi-Geodesics in the Heisenberg Group
论文作者
论文摘要
本文是本科研究项目的一部分。我们讨论了Heisenberg Group H1，这是三维空间R3，配备了两个等效度量标准之一，即Koranyi-和Carnot-Caratheodory Metric。我们表明，两个指标的曲线长度概念一致，并且存在最短的曲线，即所谓的大地测量学。
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.
