#
nLab

Riemann curvature

### Context

#### Riemannian geometry

# Contents

## Definition

For $(X,g)$ a Riemannian manifold let $\nabla_{g}$ be the corresponding Levi-Civita connection. The **Riemann curvature** $R_g$ of $(X,g)$ is the curvature $F_{\nabla_g}$ of $\nabla_g$:

$R_g := F_{\nabla_g}
\,.$

## Properties

(…)

Revised on January 14, 2013 07:47:27
by

Urs Schreiber
(137.132.3.10)