# nLab scalar curvature

Contents

### Context

#### Riemannian geometry

Riemannian geometry

# Contents

## Definition

For $(X,e)$ a (pseudo-)Riemannian manifold with smooth manifold $X$ and vielbein field $e$, its scalar curvature is the smooth function

$R(e) \in C^\infty(X, \mathbb{R})$

defined to be the trace of the Ricci tensor of $e$

$R(e) \coloneqq tr_e Ric(c) \,.$

Last revised on March 20, 2020 at 12:49:24. See the history of this page for a list of all contributions to it.