Morse theory of harmonic forms

Michael Farber, Gabriel Katz, Jerome Levine

Research output: Contribution to journalArticlepeer-review


We consider the problem of whether it is possible to improve the Novikov inequalities for closed 1-forms, or any other inequalities of a similar nature, if we assume, additionally, that the given 1-form is harmonic with respect to some Riemannian metric. We show that, under suitable assumptions, it is impossible. We use a theorem of Calabi [1], characterizing 1-forms which are harmonic with respect to some metric, in an essential way. We also study some interesting examples illustrating our results.

Original languageEnglish
Pages (from-to)469-483
Number of pages15
Issue number3
StatePublished - May 1998


FundersFunder number
U.S. Israel BinationalS cienceF oundation
National Science Foundation93-03489


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