Poisson Quasi-Nijenhuis Manifolds

Details Poisson Quasi-Nijenhuis Manifolds Poisson Quasi-Nijenhuis Manifolds

2006-02-14

arxiv.org/abs/math/0602288v2

Comm. Math. Phys. 270 (2007), no. 3, 709-725

Mathematics

Differential Geometry

18 pages, title changed, introduction rewritten, order of sections changed, references added, minor changes to body text, to a

Scientific paper

10.1007/s00220-006-0168-0

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.

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