  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.

Differential Geometry;Classical Analysis and ODEs