The torsion of spinor connections and related structures.

Klinker, Frank

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Any 7-dimensional cocalibrated $G_{2}$ -manifold admits a unique connection $\nabla$ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the $\nabla$ -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of $\nabla$ -parallel vector fields.

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Eastwood, Michael G. (2009)

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On the torsion of linear higher order connections

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For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.

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