# Did Kahler say “a long list of miracles occur”?

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

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: