English

Integration of Holomorphic Lie Algebroids

Differential Geometry 2010-05-02 v2

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.

Keywords

Cite

@article{arxiv.0803.2031,
  title  = {Integration of Holomorphic Lie Algebroids},
  author = {Camille Laurent-Gengoux and Mathieu Stienon and Ping Xu},
  journal= {arXiv preprint arXiv:0803.2031},
  year   = {2010}
}

Comments

26 pages, second part of arXiv:0707.4253 which was split into two, v2: example 3.19 and section 3.7 added

R2 v1 2026-06-21T10:21:22.089Z