Displaying similar documents to “Quaternionic contact structures in dimension 7 ”

Compatible complex structures on twistor space

Guillaume Deschamps (2011)

Annales de l’institut Fourier

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Let M be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space Z admits a natural metric. The aim of this article is to study properties of complex structures on Z which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on M (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space Z .

The intrinsic torsion of almost quaternion-Hermitian manifolds

Francisco Martín Cabrera, Andrew Swann (2008)

Annales de l’institut Fourier

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We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local Kähler forms. This gives a practical method to compute the intrinsic torsion and is applied in a number of examples. In addition we find simple characterisations of HKT and QKT geometries entirely in the exterior algebra and compute how the intrinsic...

On Solvable Generalized Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2006)

Annales de l’institut Fourier

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We give an example of a compact 6-dimensional non-Kähler symplectic manifold ( M , κ ) that satisfies the Hard Lefschetz Condition. Moreover, it is showed that ( M , κ ) is a special generalized Calabi-Yau manifold.

Conformally invariant trilinear forms on the sphere

Jean-Louis Clerc, Bent Ørsted (2011)

Annales de l’institut Fourier

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To each complex number λ is associated a representation π λ of the conformal group S O 0 ( 1 , n ) on 𝒞 ∞ ( S n - 1 ) (spherical principal series). For three values λ 1 , λ 2 , λ 3 , we construct a trilinear form on 𝒞 ∞ ( S n - 1 ) × 𝒞 ∞ ( S n - 1 ) × 𝒞 ∞ ( S n - 1 ) , which is invariant by π λ 1 ⊗ π λ 2 ⊗ π λ 3 . The trilinear form, first defined for ( λ 1 , λ 2 , λ 3 ) in an open set of ℂ 3 is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms.

An example of an asymptotically Chow unstable manifold with constant scalar curvature

Hajime Ono, Yuji Sano, Naoto Yotsutani (2012)

Annales de l’institut Fourier

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Donaldson proved that if a polarized manifold ( V , L ) has constant scalar curvature Kähler metrics in c 1 ( L ) and its automorphism group Aut ( V , L ) is discrete, ( V , L ) is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where Aut ( V , L ) is not discrete.