Vanishing theorems and string backgrounds

@article{Ivanov2000VanishingTA,
  title={Vanishing theorems and string backgrounds},
  author={Stefan Ivanov and Georgios Papadopoulos},
  journal={Classical and Quantum Gravity},
  year={2000},
  volume={18},
  pages={1089-1110}
}
We show various vanishing theorems for the cohomology groups of compact Hermitian manifolds for which the Bismut connection has a (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on compact Hermitian manifolds with vanishing first Chern class of non-Kahler type. Then we apply our results to solutions of the string equations and show that such solutions admit various… 
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