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TRANSVERSAL HARMONIC THEORY FOR TRANSVERSALLY SYMPLECTIC FLOWS

Part of: Global differential geometry Differential topology

Published online by Cambridge University Press:  01 April 2008

HONG KYUNG PAK
HONG KYUNG PAK*
Affiliation:
Faculty of Information and Science, Daegu Haany University, Kyungsan 712-715, Korea (email: hkpak@dhu.ac.kr)
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Abstract

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We develop the transversal harmonic theory for a transversally symplectic flow on a manifold and establish the transversal hard Lefschetz theorem. Our main results extend the cases for a contact manifold (H. Kitahara and H. K. Pak, ‘A note on harmonic forms on a compact manifold’, Kyungpook Math. J.43 (2003), 1–10) and for an almost cosymplectic manifold (R. Ibanez, ‘Harmonic cohomology classes of almost cosymplectic manifolds’, Michigan Math. J.44 (1997), 183–199). For the point foliation these are the results obtained by Brylinski (‘A differential complex for Poisson manifold’, J. Differential Geom.28 (1988), 93–114), Haller (‘Harmonic cohomology of symplectic manifolds’, Adv. Math.180 (2003), 87–103), Mathieu (‘Harmonic cohomology classes of symplectic manifolds’, Comment. Math. Helv.70 (1995), 1–9) and Yan (‘Hodge structure on symplectic manifolds’, Adv. Math.120 (1996), 143–154).

Keywords

transversally symplectic foliationbasic cohomologycontact manifoldsymplectic manifoldhard Lefschetz theorem

MSC classification

Secondary: 53C20: Global Riemannian geometry, including pinching 57R30: Foliations; geometric theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 233 - 245
Copyright
Copyright © 2008 Australian Mathematical Society

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