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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Killing vector fields and harmonic forms


Author: Edward T. Wright
Journal: Trans. Amer. Math. Soc. 199 (1974), 199-202
MSC: Primary 57D70; Secondary 58G10
DOI: https://doi.org/10.1090/S0002-9947-1974-0350757-2
MathSciNet review: 0350757
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Abstract: The paper is concerned with harmonic $ (p,q)$-forms on compact Kähler manifolds which admit Killing vector fields with discrete zero sets. Let $ {h^{p,q}}$ denote the dimension of the space of harmonic $ (p,q)$-forms. The main theorem states that $ {h^{p,q}} = 0,p \ne q$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0350757-2
Keywords: Killing vector field, Morse function, harmonic form, Kähler manifold
Article copyright: © Copyright 1974 American Mathematical Society