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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
7
votes
Accepted
Ricci curvature of the symplectic group
The groups $SO(n)$, $SU(n)$, and $Sp(n)$ all have Ricci tensor equal to a constant times the metric tensor. (Note: contrary to what I wrote in the question and what one may find stated in several pla …
6
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Ricci curvature of the symplectic group
Is the Ricci curvature of the compact symplectic group $Sp(n)$ bounded below by $cn$ for some constant $c > 0$ independent of $n$?
For $O(n)$ and $U(n)$ I know many references which state such a boun …