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arXiv · 0803.2031

Integration of Holomorphic Lie Algebroids

Camille Laurent-Gengoux·Mathieu Stienon·Ping Xu
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Abstract

We prove that a holomorphic Lie algebroid is integrable if, and only if, its underlying real Lie algebroid is integrable. Thus the integrability criteria of Crainic-Fernandes do also apply in the holomorphic context without any modification. As a consequence we give another proof of the following theorem: a holomorphic Poisson manifold is integrable if, and only if, its real (or imaginary) part is integrable as a real Poisson manifold.

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Camille Laurent-Gengoux, Mathieu Stienon, Ping Xu. 2008-03-13. Integration of Holomorphic Lie Algebroids. https://doi.org/10.1007/s00208-009-0388-7

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