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Poisson Quasi-Nijenhuis Manifolds

Mathieu Stienon·Ping Xu
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Abstract

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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BibTeXRIS

Mathieu Stienon, Ping Xu. 2006-09-20. Poisson Quasi-Nijenhuis Manifolds. https://doi.org/10.1007/s00220-006-0168-0

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