Poisson Quasi-Nijenhuis Manifolds
Abstract
Description
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.
18 pages, title changed, introduction rewritten, order of sections changed, references added, minor changes to body text, to appear in Comm. Math. Phys
18 pages, title changed, introduction rewritten, order of sections changed, references added, minor changes to body text, to appear in Comm. Math. Phys