Timeline for Geometric and holomorphic structure of $\mathbb{C} \rtimes \mathbb{C} \setminus \{ 0 \}$
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| May 16, 2017 at 9:34 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
edited body
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| May 16, 2017 at 8:58 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| S May 16, 2017 at 3:56 | history | suggested | jeq | CC BY-SA 3.0 |
Corrected some English typos.
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| May 16, 2017 at 3:21 | review | Suggested edits | |||
| S May 16, 2017 at 3:56 | |||||
| May 13, 2017 at 23:34 | comment | added | Ali Taghavi | @YCor are there some vector fields in its Lie algebra which foliate G with closed geodesics? | |
| May 13, 2017 at 23:11 | comment | added | YCor | ...if it's homotopic to the identity among holomorphic group automorphisms | |
| May 13, 2017 at 22:52 | comment | added | Ali Taghavi | @YCor regarding the automorphism group, are you saying every bi holomirphic map on G is an inner group automorphism provided it is homotopic to identity? | |
| May 13, 2017 at 22:50 | comment | added | Ali Taghavi | @YCor yes i was incorrect | |
| May 13, 2017 at 22:39 | comment | added | YCor | No, the group you mention is commutative. | |
| May 13, 2017 at 22:35 | comment | added | Ali Taghavi | @YCor I think G is isomorphic to all matrices with (a, b,0, a). A on diagonal. But could you please explain on remaining part of your comment?(or please give a reference) | |
| May 13, 2017 at 21:42 | comment | added | YCor | $G$ is isomorphic to the group of upper triangular matrices in $\mathrm{PGL}_2(\mathbf{C}$; it acts transitively by isometries (fixing a boundary point) on the 3-dimensional hyperbolic space and thus can probably be seen inside its unit tangent bundle. Computing the automorphism group is an exercise using the Lie algebra; in particular its unit component is made of the inner automorphisms. | |
| May 13, 2017 at 21:30 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| May 13, 2017 at 21:13 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| May 13, 2017 at 21:06 | history | asked | Ali Taghavi | CC BY-SA 3.0 |