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.
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