Vezzoni, Luigi A note on infinitesimal deformations of symplectic half-flat structures. (English) Zbl 1179.53035 Int. Math. Forum 3, No. 25-28, 1313-1326 (2008). Let \(M\) be a 6-dimensional smooth manifold. A half-flat structure on \(M\) is an \(\text{SU(3)}\)-structure whose defining forms \((\omega, \psi_+)\in\wedge^2M\oplus\wedge^3M\) satisfy \(d\omega\wedge\omega=0\) and \(d\psi_+=0\). A half-flat structure \((\omega, \psi_+)\) is symplectic half-flat if \(\omega\) is a symplectic form. A symplectic form \(\omega\) satisfies the hard Lefschetz condition if the map \(\wedge\omega^p:\wedge^{3-p}M\to\wedge^{3+p}M\), defined by \(\gamma\mapsto\omega^p\wedge\gamma\), induces an isomorphism in cohomology for \(p=1,2,3\).It is shown in this work that the moduli space of infinitesimal deformations of symplectic half-flat structure satisfying the hard Lefschetz condition has finite dimension. The technics used are the ones introduced by R. Goto in [Int. J. Math. 15, No. 3, 211–257 (2004; Zbl 1046.58002), arXiv:math/0108002]. Reviewer: Valeriy A. Yumaguzhin (Pereslavl’-Zalesskiy) MSC: 53C10 \(G\)-structures 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D05 Symplectic manifolds (general theory) 32G07 Deformations of special (e.g., CR) structures Keywords:\(G\)-structures; half-flat structures; infinitesimal deformations; moduli space Citations:Zbl 1046.58002 PDFBibTeX XMLCite \textit{L. Vezzoni}, Int. Math. Forum 3, No. 25--28, 1313--1326 (2008; Zbl 1179.53035) Full Text: Link