Timeline for Finding the metric associated with a group action
Current License: CC BY-SA 3.0
5 events
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Jun 27, 2017 at 3:10 | comment | added | Igor Belegradek | The isometry group is Lie group that acts properly and conversely, any proper effective action of a Lie group is isometric in some Riemannian metric. The former is proven e.g. in Kobayashi-Nomidzy textbook, vol I, Theorem I.4.7. The latter is due to Palais Theorem 4.3.1 in [On the existence of slices for actions of non-compact Lie groups, Ann. of Math. 73 (1961), 295–323.] See vmm.math.uci.edu/ExistenceOfSlices.pdf. | |
Jun 27, 2017 at 1:52 | comment | added | Feng Hao | If $G$ is compact, there is always a $G$-invariant metric over $M$, by integration over $G$. For General $G$, it should not be true | |
Jun 27, 2017 at 0:53 | history | edited | user11881 | CC BY-SA 3.0 |
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Jun 27, 2017 at 0:48 | review | First posts | |||
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Jun 27, 2017 at 0:45 | history | asked | user11881 | CC BY-SA 3.0 |