Hard Lefschetz Theorem for Sasakian manifolds

Autor:	Montano, Beniamino Cappelletti, De Nicola, Antonio, Yudin, Ivan
Rok vydání:	2013
Předmět:	Mathematics - Differential Geometry Mathematics - Symplectic Geometry Primary 53C25 53D35
Zdroj:	J. Differential Geom. 101 (2015), 47-66
Druh dokumentu:	Working Paper
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:	arXiv
Externí odkaz:	http://arxiv.org/abs/1306.2896 Zobrazit plný text záznamu View this record from Arxiv