Poisson Quasi-Nijenhuis Manifolds
摘要
We introduce the notion of Poisson quasi-Nijenhuis manifolds generalizing the Poisson-Nijenhuis manifolds of Magri-Morosi. We also investigate the integration problem of Poisson quasi-Nijenhuis manifolds. In particular, we prove that, under some topological assumption, Poisson (quasi)-Nijenhuis manifolds are in one-one correspondence with symplectic (quasi)-Nijenhuis groupoids. As an application, we study generalized complex structures in terms of Poisson quasi-Nijenhuis manifolds. We prove that a generalized complex manifold corresponds to a special class of Poisson quasi-Nijenhuis structures. As a consequence, we show that a generalized complex structure integrates to a symplectic quasi-Nijenhuis groupoid recovering a theorem of Crainic.
引用
@article{arxiv.math/0602288,
title = {Poisson Quasi-Nijenhuis Manifolds},
author = {Mathieu Stienon and Ping Xu},
journal= {arXiv preprint arXiv:math/0602288},
year = {2008}
}
备注
18 pages, title changed, introduction rewritten, order of sections changed, references added, minor changes to body text, to appear in Comm. Math. Phys