Hard Lefschetz Theorem for Sasakian manifolds
| Autor: | Ivan Yudin, Antonio De Nicola, Beniamino Cappelletti-Montano |
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| Rok vydání: | 2013 |
| Předmět: |
Mathematics - Differential Geometry
Algebra and Number Theory Dimension (graph theory) Contact manifolds Mathematics::Algebraic Topology Manifold Sasakian manifold Combinatorics Primary 53C25 53D35 Sasakian manifolds Differential Geometry (math.DG) Mathematics - Symplectic Geometry Hard Lefschetz Theorem Differential Geometry De Rham cohomology FOS: Mathematics Symplectic Geometry (math.SG) Geometry and Topology Isomorphism Mathematics::Differential Geometry Exterior algebra Mathematics::Symplectic Geometry Analysis Mathematics |
| Zdroj: | Scopus-Elsevier J. Differential Geom. 101, no. 1 (2015), 47-66 |
| DOI: | 10.48550/arxiv.1306.2896 |
| Popis: | We prove that on a compact Sasakian manifold $(M, \eta, g)$ of dimension $2n+1$, for any $0 \le p \le n$ 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. Comment: 19 pages, 1 figure, accepted for publication in the Journal of Differential Geometry |
| Databáze: | OpenAIRE |
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