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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