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In general, the product of two harmonic differential forms is not harmonic. However, for Kähler manifolds, the product of two harmonic forms is harmonic. What is a counterexample for the first statement and how do I prove the second? Thanks.

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    Either Kähler or Kaehler is a correct spelling, but if Kahler were correct, then it would be pronounced differently. "Kähler" and "Kaehler" are for all reasonable purposes the same spelling; "Kahler" is different.2012-02-09
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    @Michael Hardy: So how is "Kaehler" pronounced anyway? (I've always wondered...)2012-02-09
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    "äh" is pretty close to the "long-a" sound in English.2012-02-09

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