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The intrinsic torsion of almost quaternion-Hermitian manifolds

Francisco Martín Cabrera, Andrew Swann (2008)

Annales de l’institut Fourier

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 torsion...

The Srní lectures on non-integrable geometries with torsion

Ilka Agricola (2006)

Archivum Mathematicum

This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...

The structure tensor and first order natural differential operators

Piotr Kobak (1992)

Archivum Mathematicum

The notion of a structure tensor of section of first order natural bundles with homogeneous standard fibre is introduced. Properties of the structure tensor operator are studied. The universal factorization property of the structure tensor operator is proved and used for classification of first order * -natural differential operators D ̲ : T × T ̲ → T ̲ for n ≥ 3 .

The Tanaka-Webster connection for almost 𝒮 -manifolds and Cartan geometry

Antonio Lotta, Anna Maria Pastore (2004)

Archivum Mathematicum

We prove that a CR-integrable almost 𝒮 -manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost 𝒮 -structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost 𝒮 -structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal...

Universal spaces for manifolds equipped with an integral closed k -form

Hông-Vân Lê (2007)

Archivum Mathematicum

In this note we prove that any integral closed k -form φ k , k ≥ 3 , on a m-dimensional manifold M m , m ≥ k , is the restriction of a universal closed k -form h k on a universal manifold U d ( m , k ) as a result of an embedding of M m to U d ( m , k ) .

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