Parallel spinors and connections with skew-symmetric torsion in string theory

@article{Friedrich2001ParallelSA,
  title={Parallel spinors and connections with skew-symmetric torsion in string theory},
  author={Thomas Friedrich and Stefan Ivanov},
  journal={Asian Journal of Mathematics},
  year={2001},
  volume={6},
  pages={303-336}
}
We describe all almost contact metric, almost hermitian and G2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5,6 and 7. 
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315 Citations

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