2006/02/28 by Mathieu Stiénon, Mathieu Stienon, Ping Xu · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #hep-th #math.DG #math.SG
paper · pdf · doi:10.1007/s00220-006-0168-0
published as Comm. Math. Phys. 270 (2007), no. 3, 709-725 · 18 pages, title changed, introduction rewritten, order of sections changed, references added, minor changes to body text, to appear in Comm. Math. Phys
arxiv created 2006/09/20 · openalex publication_date 2007/01/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.