# Connections with torsion, parallel spinors and geometry of Spin(7) manifolds

@article{Ivanov2001ConnectionsWT, title={Connections with torsion, parallel spinors and geometry of Spin(7) manifolds}, author={Stefan Ivanov}, journal={Mathematical Research Letters}, year={2001}, volume={11}, pages={171-186} }

We show that on every Spin(7)-manifoldthere always exists a unique linear connection with totally skew-symmetric torsion preserving a nontrivial spinor andthe Spin(7) structure. We express its torsion andthe Riemannian scalar cur- vature in terms of the fundamental 4-form. We present an explicit formula for the Riemannian covariant derivative of the fundamental 4-form in terms of its exterior differential. We show the vanishing of the ˆ A-genus andobtain a linear relation between Betti numbers…

## 90 Citations

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