TY - JOUR

T1 - Morse theory of harmonic forms

AU - Farber, Michael

AU - Katz, Gabriel

AU - Levine, Jerome

N1 - Funding Information:
Acknowledgements-Wweo uldl ike to thankR obertK otiugaf or bringingt hew ork of Calabit o our attentiona nd for many stimulatingd iscussionsT. he researchw as supportedb y U.S. Israel BinationalS cienceF oundation Grants 940029a9n d 9400073a,n d NSF Grant 93-03489.

PY - 1998/5

Y1 - 1998/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032063464&partnerID=8YFLogxK

U2 - 10.1016/S0040-9383(97)82730-9

DO - 10.1016/S0040-9383(97)82730-9

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AN - SCOPUS:0032063464

SN - 0040-9383

VL - 37

SP - 469

EP - 483

JO - Topology

JF - Topology

IS - 3

ER -