Abstract
We construct examples of symplectic half-flat manifolds on compact quotients of solvable Lie groups. We prove that the Calabi-Yau structures are not rigid in the class of symplectic half-flat structures. Moreover, we provide an example of a compact 6-dimensional symplectic half-flat manifold whose real part of the complex volume form is d-exact. Finally we discuss the 4-dimensional case.
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This work was supported by the Projects M.I.U.R. “Geometric Properties of Real and Complex Manifolds”, “Riemannian Metrics and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M.
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Tomassini, A., Vezzoni, L. On symplectic half-flat manifolds. manuscripta math. 125, 515–530 (2008). https://doi.org/10.1007/s00229-007-0158-3
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DOI: https://doi.org/10.1007/s00229-007-0158-3