Timeline for The differential of the Gauss normal map from a Lie algebraic view point
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2018 at 8:42 | vote | accept | Ali Taghavi | ||
| S Aug 20, 2018 at 8:42 | history | bounty ended | Ali Taghavi | ||
| S Aug 20, 2018 at 8:42 | history | notice removed | Ali Taghavi | ||
| S Aug 14, 2018 at 8:02 | history | bounty started | Ali Taghavi | ||
| S Aug 14, 2018 at 8:02 | history | notice added | Ali Taghavi | Authoritative reference needed | |
| Aug 14, 2018 at 7:53 | comment | added | Ali Taghavi | @DeaneYang Dear prof. Yang I am sorry if my question is elementary. To be honnest I did not understand a relation between my question and the part of your statement that "......this familly consist of either whole morphisms or 0 or identity.." I would appreciate if you more explain. | |
| Aug 11, 2018 at 18:18 | answer | added | Deane Yang | timeline score: 8 | |
| Aug 11, 2018 at 9:29 | comment | added | Ali Taghavi | @DeaneYang so my question can be read, when the shape operator generate a lie algebra morphism on the space of vector fields on our surface?When its range is a Lie algebra? | |
| Aug 11, 2018 at 3:36 | comment | added | Deane Yang | that is correct. The eigenvalues of the shape operator are the principal curvatures. And the shape operator of the cylinder is neither the identity map nor zero. | |
| Aug 11, 2018 at 3:06 | comment | added | Ali Taghavi | @DeaneYang I think the eigenvalues of $dN$ are principal curvatures, then for cylinder it is neither identically zero nor "identity". Right? | |
| Aug 10, 2018 at 21:38 | comment | added | Deane Yang | $dN$ is known as the shape operator and is a $(1,1)$-tensor, i.e. an endomorphism of $T_*S$. Based on a quick back-of-the-envelope calculation, I believe that $dN$ has to be either the identity map or the zero map. In the first case, it is a sphere. In the second, it is a flat surface. | |
| Aug 10, 2018 at 17:58 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 117 characters in body
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| Aug 10, 2018 at 13:58 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 27 characters in body
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| Aug 10, 2018 at 12:18 | history | edited | Ali Taghavi |
I add a tag.
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| Aug 10, 2018 at 11:54 | history | asked | Ali Taghavi | CC BY-SA 4.0 |