Abstract
Let X be a connected complex manifold of dimension \(\ge 3\) and M a smooth compact Levi-flat real hypersurface in X. We show that the normal bundle to the Levi foliation does not admit a Hermitian metric with positive curvature along the leaves. This generalizes a result obtained by Brunella.
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Acknowledgements
I wish to express my thanks to Stefan Nemirovski for his contribution to this paper: the construction of the Kähler metric in the proof of Proposition 8.1 was essentially his idea. I would also like to thank Masanori Adachi and Takeo Ohsawa not only for their great interest, but also for many helpful remarks improving the paper. The research on this project was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Grant BR 3363/2-2).
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Communicated by Ngaiming Mok.
