# Chapter 21 Riemannian Manifolds

In this chapter, we narrow the scope from semi‐Riemannian manifolds to Rie‐ mannian manifolds and examine selected earlier topics in that more specialized setting.

## 21.1 Geodesics and Curvature on Riemannian Manifolds

Here is the promised generalization of Theorem 19.9.3 to Riemannian manifolds.

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