# 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…

## 62 Citations

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## References

SHOWING 1-10 OF 55 REFERENCES

### Curvature properties of twistor spaces of quaternionic Kähler manifolds

- Mathematics
- 1998

We present a study of natural almost Hermitian structures on twistor spaces of quaternionic Kahler manifolds. This is used to supply (4n + 2)-dimensional examples (n > 1) of symplec tic non-Kähler…

### Geometry of Hyper-Kähler Connections with Torsion

- Mathematics
- 2000

Abstract:The internal space of a N = 4 supersymmetric model with Wess–Zumino term has a connection with totally skew-symmetric torsion and holonomy in SP(n). We study the mathematical background of…