<math>\begin{align}   & \left\{ \begin{align}   & m{\alpha }'\tau \hbar \varepsilon \mu \alpha \mathbf{T}ic\varsigma  \\   & \text{      }\And  \\   & \text{  }\mathsf{\mathcal{P}}\pi y\sigma \mathbf{I}\subset \mathbf{S} \\  \end{align} \right\} \\   & \text{    }Wikia \\  \end{align}</math>

Riemann Curvature Tensor

118articles on
the Psi Epsilon Wikia
Add New Page
Comments0 Share


This article is a stub. You can help Mathematics and Physics Wiki by expanding it.

The Riemann Curvature Tensor is a tensor in Riemannian Geometry that describes the curvature of a manifold. Specifically, it measures the failure (known as the holonomy) of the ability of parallel transport to retain the direction of a vector in a space. In other words, it can be calculated as:


IdentitiesEdit this section

Correction to Proof of the Zeroth Bianchi Identity08:13

Correction to Proof of the Zeroth Bianchi Identity

More on Bianchi Identities14:57

More on Bianchi Identities

More on Bianchi Identities-014:57

More on Bianchi Identities-0

The definition of the Riemann Curvature Tensor immediately implies that:


And therefore;


Now, below are some other identities:

R_{\mu\nu(\rho\sigma)} = 0 See [1] .

First Bianchi Identity [2] .

Second Bianchi Identity [3] .

ReferencesEdit this section

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.