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September 2015 Hard Lefschetz theorem for Sasakian manifolds
Beniamino Cappelletti-Montano, Antonio De Nicola, Ivan Yudin
J. Differential Geom. 101(1): 47-66 (September 2015). DOI: 10.4310/jdg/1433975483

Abstract

We prove that on a compact Sasakian manifold $(M,\eta, g)$ of dimension $2n + 1$, for any $0 \leq p \leq n$ the wedge product with $\eta \wedge (d \eta)^p$ defines an isomorphism between the spaces of harmonic forms $\Omega^{n-p}_{\Delta}(M)$ and $\Omega^{n+p+1}_{\Delta}(M)$. Therefore it induces an isomorphism between the de Rham cohomology spaces $H^{n-p}(M)$ and $H^{n+p+1}(M)$. Such isomorphism is proven to be independent of the choice of a compatible Sasakian metric on a given contact manifold. As a consequence, an obstruction for a contact manifold to admit Sasakian structures is found.

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Beniamino Cappelletti-Montano. Antonio De Nicola. Ivan Yudin. "Hard Lefschetz theorem for Sasakian manifolds." J. Differential Geom. 101 (1) 47 - 66, September 2015. https://doi.org/10.4310/jdg/1433975483

Information

Published: September 2015
First available in Project Euclid: 10 June 2015

zbMATH: 1322.58002
MathSciNet: MR3356069
Digital Object Identifier: 10.4310/jdg/1433975483

Rights: Copyright © 2015 Lehigh University

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Vol.101 • No. 1 • September 2015
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