Pseudo-Poisson Nijenhuis Manifolds

Tomoya Nakamura

    Research output: Contribution to journal › Article

    Abstract

    We introduce the notion of pseudo-Poisson Nijenhuis manifolds. These manifolds are generalizations of Poisson Nijenhuis manifolds defined by Magri and Morosi [13]. We show that there is a one-to-one correspondence between the pseudo-Poisson Nijenhuis manifolds and certain quasi-Lie bialgebroid structures on the tangent bundle as in the case of Poisson Nijenhuis manifolds by Kosmann-Schwarzbach [7]. For that reason, we expand the general theory of the compatibility of a 2-vector field and a (1, 1)-tensor. We also introduce pseudo-symplectic Nijenhuis structures, and investigate properties of them. In particular, we show that those structures induce twisted Poisson structures [18].

    Original languageEnglish
    Pages (from-to)121-135
    Number of pages15
    JournalReports on Mathematical Physics
    Volume82
    Issue number1
    DOIs
    Publication statusPublished - 2018 Aug 1

    Fingerprint

    Siméon Denis Poisson
    Poisson Structure
    Tangent Bundle
    One to one correspondence
    tangents
    Compatibility
    compatibility
    Expand
    bundles
    Vector Field
    Tensor
    tensors

    Keywords

    • Poisson
    • Poisson–Nijenhuis
    • quasi-Poisson
    • twisted Poisson

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Pseudo-Poisson Nijenhuis Manifolds. / Nakamura, Tomoya.

    In: Reports on Mathematical Physics, Vol. 82, No. 1, 01.08.2018, p. 121-135.

    Research output: Contribution to journal › Article

    Nakamura, T 2018, 'Pseudo-Poisson Nijenhuis Manifolds', Reports on Mathematical Physics, vol. 82, no. 1, pp. 121-135. https://doi.org/10.1016/S0034-4877(18)30074-0
    Nakamura T. Pseudo-Poisson Nijenhuis Manifolds. Reports on Mathematical Physics. 2018 Aug 1;82(1):121-135. https://doi.org/10.1016/S0034-4877(18)30074-0
    Nakamura, Tomoya. / Pseudo-Poisson Nijenhuis Manifolds. In: Reports on Mathematical Physics. 2018 ; Vol. 82, No. 1. pp. 121-135.
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