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Gaussian curvature, mean curvature, sectional curvature, scalar curvature, curvature tensors (Riemann, Ricci, Weyl)

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3 answers
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Curvature of a Lie group

Since a lie group is a manifold with the structure of a continuous group, then each point of the manifold [Edit: provided we fix a metric, for example an invariant or bi-invariant one] has some scalar curvature … Question [Edited] Is there a nice formula which expresses the scalar curvature at a point of the manifold in terms of the lie algebra of the group? …
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