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arXiv · 1703.09408

Pseudo-Poisson Nijenhuis manifolds

Tomoya Nakamura
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Abstract

We introduce the notion of pseudo-Poisson Nijenhuis manifolds. These manifolds are generalizations of Poisson Nijenhuis manifolds by Magri and Morosi \cite{MM}. We show that any pseudo-Poisson Nijenhuis manifold has an associated quasi-Lie bialgebroid as in the case of Poisson quasi-Nijenhuis manifolds by Sti$\acute{\mathrm{e}}$non and Xu \cite{SX}. Hence, since a quasi-Lie bialgebroid has an associated Courant algebroid, we have new materials to construct Courant algebroids. In the "nondegenerate" case, we show that the conditions of pseudo-Poisson Nijenhuis structures can be reduced. Therefore we can provide lots of non-trivial examples of pseudo-Poisson Nijenhuis manifolds.

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Tomoya Nakamura. 2017-03-28. Pseudo-Poisson Nijenhuis manifolds. https://doi.org/10.1016/s0034-4877(18)30074-0

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