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 language | English |
|---|---|
| Pages (from-to) | 121-135 |
| Number of pages | 15 |
| Journal | Reports on Mathematical Physics |
| Volume | 82 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2018 Aug 1 |
Keywords
- Poisson
- Poisson–Nijenhuis
- quasi-Poisson
- twisted Poisson
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
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Cite this
Nakamura, T. (2018). Pseudo-Poisson Nijenhuis Manifolds. Reports on Mathematical Physics, 82(1), 121-135. https://doi.org/10.1016/S0034-4877(18)30074-0