Displaying similar documents to “Differential geometry of quaternionic manifolds”

The Srní lectures on non-integrable geometries with torsion

Ilka Agricola (2006)

Archivum Mathematicum

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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...

On the characteristic connection of gwistor space

Rui Albuquerque (2013)

Open Mathematics

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We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.

The principal prolongation of first order G -structures

Slovák, Jan

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The author uses the concept of the first principal prolongation of an arbitrary principal filter bundle to develop an alternative procedure for constructing the prolongations of a class of the first-order G -structures. The motivation comes from the almost Hermitian structures, which can be defined either as standard first-order structures, or higher-order structures, but if they do not admit a torsion-free connection, the classical constructions fail in general.