# 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}
}
• S. Ivanov
• Published 20 November 2001
• Mathematics
• Mathematical Research Letters
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…

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