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I've been reading Moroianu's Kahler geometry notes and found a unattributed quote that says that if the Kahler properties hold, then "a long list of miracles occur"

I am guessing that this quote belongs to Kahler himself, but I can't back this up. Does anyone know?

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I have no idea, however: cartoonbank.com/… –  Will Jagy Jul 26 '11 at 21:14
For those who want to look themselves: dx.doi.org/10.1007/BF02940642 –  Theo Buehler Jul 27 '11 at 0:19

3 Answers 3

up vote 10 down vote accepted

I will make a CW answer to collect together some information.

Igor Rivin found a published text containing the relevant phrase. It is in "The unabated vitality of Kählerian geometry," by Jean-Pierre Bourguignon which is included in the collected works of Kähler (Kähler, Mathematische Werke/Mathematical Works, edited by Berndt and Riemenschneider, 2003).

The relevant pasage is (from the text of Bourguignon where 'he' refers to Kähler):

Quoting his terms, the case $d \omega = 0$ presents itself as "a remarkable exception". This is the condition he supposes throughout the paper whose purpose it is to describe a long list of miracles occuring then.

This suggest to me that while Bourguignon is first quoting Kähler (the "a remarkable exception") he then stops quoting (and a new sentence started) and describes in his [Bourguignon's] own words the list of result/properties obtained by Kähler as miracolous.

Side note: in this text there are some other verbatim quotes and they are under quotation marks; so except if Bourguignon inadvertently omitted them, he is not quoting.

Furthermore, the paper of Kähler in question "Über eine bemerkenswerte Hermitesche Metrik" does not seem to contain such a phrase (cf. csar). I also searched the above mentioned book for appropriate terms (miracles, the German analog Wunder, and also Mir* in case he should have used Mirakel, which exists but is a bit rare); this did not turn up anything, besides what is mentioned above.

Therefore it seems likely to me that this 'miracles' are due to Bourguignon and not Kähler; and, Moroianu is sort-of quoting Bourguignon. The time-line might seem a bit short, the notes being from 2003 as well as the book, however in view of the fact that Moroianu is a former student of Bourguignon this seems much less surprising, and perhaps even reinforces the idea that Moroianu is quoting Bourguignon.

Final note: in case somebody wants to make really sure, Moroianu is a (it seems now inactive) MO user, so he might, if made aware of the need, give an authentic account.

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I believe the answer is yes, see:


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I only checked the link briefly, but why do you think 'yes' from this link? The text is by Bourguignon; the exact quotes there seem to be under quotation marks and the relevant passage is not. Perhaps, Moroianu is quoting Bourguignon; in principle, not at all unlikely. I checked the relevant paper by Kähler very roughly and did not see anything. –  quid Jul 26 '11 at 23:35
It sounded like Bourguignon was quoting or paraphrasing, but perhaps he is not quoting or paraphrasing Kahler himself? –  Igor Rivin Jul 27 '11 at 1:01
I have no information beyond the text but my guess is B. is not quoting or paraphrasing anybody, I recall the text: ' Quoting his terms, the case d omega = 0 presents itself as "a remarkable exception". This is the condition he supposes throughout the paper whose purpose it is to describe a long list of miracles occuring then.' Where 'he' is Kähler and the 'rem. ex.' is thus Kähler. But there are no quotes for the 'miracles' as opposed to the 'rem. exception' and there is a period in between. And thus I'd assume it is B. who describes the properties/results obtained by Kähler as miracles. –  quid Jul 27 '11 at 1:35
Well, that certainly makes sense. –  Igor Rivin Jul 27 '11 at 2:05

Following quid's comment (I don't have the reputation to comment), assuming Über eine bemerkenswerte Hermitesche Metrik is the place to look, it doesn't appear to be in there. The "long list of miracles" does seem to be apparent in a quick skim of the paper, though (and a naive skim at that--I just read the words, not the content).

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