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Transactions of the American Mathematical Society

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

 

 

Nonexistence of nontrivial $ cm''$-harmonic 1-forms on a complete foliated Riemannian manifold


Author: Haruo Kitahara
Journal: Trans. Amer. Math. Soc. 262 (1980), 429-435
MSC: Primary 57R30; Secondary 58A14
DOI: https://doi.org/10.1090/S0002-9947-1980-0586726-X
MathSciNet review: 586726
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Abstract: We study the nonexistence of nontrivial $ \square''$-harmonic 1-forms on a complete foliated riemannian manifold with positive definite Ricci curvature. It is well known that the harmonic 1-form on a compact and orientable riemannian manifold with positive definite Ricci curvature is trivial. Our main theorem is an extension of this fact in the complete foliated riemannian case.


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DOI: https://doi.org/10.1090/S0002-9947-1980-0586726-X
Keywords: Bundle-like metric, second connection, $ \square''$-harmonic form
Article copyright: © Copyright 1980 American Mathematical Society