Timeline for Hsiung on the Complex Structure of $S^6$
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Aug 12, 2017 at 17:14 | comment | added | YangMills | @RobertBryant Thank you very much, I was not aware of this! | |
| Aug 12, 2017 at 12:34 | comment | added | Robert Bryant | @YangMills: As for the error(s) in Adler's 1969 paper, the main breakdown occurs because his whole argument relies on Proposition 2 from his earlier paper The Second Fundamental Form of a Kähler Metric, Amer. J. Math. 89 (1967), 260–274, and this Proposition is simply wrong. His error is that he assumes that the first Chern form of the LC-connection of an Hermitian metric on a complex manifold is necessarily of type $(1,1)$. (He just writes that it's "a known property", with no argument.) This false claim is crucial for his construction of a Kähler metric when his inequality is satisfied. | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 7, 2013 at 23:34 | answer | added | Guan | timeline score: 3 | |
| S Sep 1, 2012 at 19:15 | vote | accept | HeWhoHungers | ||
| Jul 12, 2012 at 0:51 | answer | added | Robert Bryant | timeline score: 48 | |
| Jul 11, 2012 at 6:45 | vote | accept | HeWhoHungers | ||
| S Sep 1, 2012 at 19:15 | |||||
| Jul 11, 2012 at 3:22 | comment | added | Deane Yang | YangMills, that might be right. Thanks! | |
| Jul 11, 2012 at 2:57 | comment | added | YangMills | @Deane: maybe you were thinking about S.S.Chern's last preprint (2004)? It was never published, but you might have seen it. | |
| Jul 11, 2012 at 2:49 | answer | added | YangMills | timeline score: 14 | |
| Jul 11, 2012 at 2:45 | comment | added | Deane Yang | I vaguely recall knowing about 3 separate published proofs that were not taken seriously by other experts but I don't remember the third one anymore. I've never found anyone who could explain to me what the error in either Adler's or Hsiung's proof is. But I never thought of asking Siu. | |
| Jul 10, 2012 at 22:08 | comment | added | YangMills | Having said this, I don't know exactly where Hsiung's mistake is, I will search a bit and see what I can find. | |
| Jul 10, 2012 at 22:07 | comment | added | YangMills | You might ask the same question about the paper of A.Adler "The second fundamental forms of $S^{6}$ and $P^{n}({\bf C})$", Amer. J. Math. 91 (1969) 657–670, which claims to prove the same result. In this case Steve Krantz says here books.google.com/… that he saw a paper of Y.T.Siu which explains precisely where Adler's error is. However, I couldn't find any paper of Siu where this is discussed. | |
| Jul 10, 2012 at 20:30 | history | asked | HeWhoHungers | CC BY-SA 3.0 |