For $(X,e)$ a (pseudo-)Riemannian manifold with smooth manifold $X$ and vielbein field $e$, its scalar curvature is the smooth function
defined to be the trace of the Ricci tensor of $e$
The product of the scalar curvature with the volume form is the Lagrangian of the theory (physics) of gravity. The corresponding action functional is the Einstein-Hilbert action.
curvature in Riemannian geometry |
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Riemann curvature |
Ricci curvature |
scalar curvature |
sectional curvature |
p-curvature |
Last revised on April 25, 2018 at 03:17:06. See the history of this page for a list of all contributions to it.