# product of harmonic forms in a kähler manifold

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. –  Michael Hardy Feb 9 '12 at 3:43
@Michael Hardy: So how is "Kaehler" pronounced anyway? (I've always wondered...) –  Jesse Madnick Feb 9 '12 at 4:39
"äh" is pretty close to the "long-a" sound in English. –  Michael Hardy Feb 9 '12 at 16:38