Introduction to Riemannian Manifolds pp 85-113 | Cite as

# Connections

Chapter

First Online:

## Abstract

Before defining a notion of curvature that makes sense on arbitrary Riemannian manifolds, we need to study *geodesics*, the generalizations to Riemannian manifolds of straight lines in Euclidean space. In this chapter, we introduce a new geometric construction called a *connection*, which is an essential tool for defining geodesics.

## Copyright information

© Springer International Publishing AG 2018