Displaying similar documents to “The Srní lectures on non-integrable geometries with torsion”

On types of non-integrable geometrie

Friedrich, Thomas

Similarity:

A G-structure on a Riemannian manifold is said to be integrable if it is preserved by the Levi-Civita connection. In the presented paper, the following non-integrable G-structures are studied: SO(3)-structures in dimension 5; almost complex structures in dimension 6; G 2 -structures in dimension 7; Spin(7)-structures in dimension 8; Spin(9)-structures in dimension 16 and F 4 -structures in dimension 26. G-structures admitting an affine connection with totally skew-symmetric torsion are characterized....

A classification of the torsion tensors on almost contact manifolds with B-metric

Mancho Manev, Miroslava Ivanova (2014)

Open Mathematics

Similarity:

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.

On the characteristic connection of gwistor space

Rui Albuquerque (2013)

Open Mathematics

Similarity:

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.

Lorentzian manifolds with special holonomy and parallel spinors

Leistner, Thomas

Similarity:

The author studies the holonomy group of a simply connected indecomposable and reducible Lorentzian spin manifold under the condition that they admit parallel spinors. He shows that there are only two possible situations: either the manifold is a so-called Brinkmann wave or it has Abelian holonomy and is a pp-manifold – a generalization of a plane-wave. The author gives also sufficient conditions for a Brinkmann wave to have as holonomy the semidirect product of holonomy group of a Riemannian...