Poisson Quasi-Nijenhuis Manifolds |
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Authors: | Mathieu Stiénon Ping Xu |
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Institution: | 1.Departement Mathematik,E.T.H. Zürich,Zürich,Switzerland;2.Department of Mathematics,Pennsylvania State University,University Park,USA |
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Abstract: | We introduce the notion of Poisson quasi-Nijenhuis manifolds generalizing 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.
Francqui fellow of the Belgian American Educational Foundation.
Research supported by NSF grant DMS03-06665 and NSA grant 03G-142. |
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