Differential Geometry of Curves and Surfaces pp 247-318 | Cite as

# Geodesics

Chapter

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## Abstract

The most fundamental concept for studying the geometry of \(\mathbb{R}^{2}\) is a straight line. The goal of this chapter is to generalize this fundamental notion from \(\mathbb{R}^{2}\) to arbitrary regular surfaces. Although most surfaces curve in such a way that they don’t contain any straight lines, they do contain curves called *geodesics*, which will turn out to share many important characterizing properties of straight lines.

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© Springer International Publishing Switzerland 2016