Timeline for Bi invariant Riemannian metric on a Lie Group
Current License: CC BY-SA 3.0
7 events
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| Nov 20, 2013 at 8:38 | comment | added | YCor | @user42999: your statement "if $G/H$ has invariant Riem. metric then $H$ is compact" is false. 2 counterexamples: (1) $G$ not compact, $H=G$; (2) $G$ arbitrary, $H$ any infinite discrete subgroup: this second example shows that your statement is false even if $G$ acts faithfully on $G/H$. | |
| Nov 19, 2013 at 23:03 | comment | added | Misha | That's what I wrote. On the other hand, very few connected Lie groups admit biinvariant metrics: products of abelian and compact groups. | |
| Nov 19, 2013 at 22:57 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Language editing, and added top-level tags.
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| Nov 19, 2013 at 22:51 | comment | added | user42999 | So the first claim is true even if H is not compact @Misha ? | |
| Nov 19, 2013 at 22:47 | review | First posts | |||
| Nov 19, 2013 at 22:58 | |||||
| Nov 19, 2013 at 22:33 | comment | added | Misha | If $G$ admits a biinvariant Riemannian metric $ds^2$, then projection fo $ds^2$ to $G/H$ is left-invariant under the action of $G$. As for your other question, think about abelian groups. | |
| Nov 19, 2013 at 22:29 | history | asked | user42999 | CC BY-SA 3.0 |