nLab Riemann curvature

Context

Riemannian geometry

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

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Revised on March 18, 2015 15:04:19 by Urs Schreiber (80.92.246.195)