On some generalizations of a Poisson Nijenhuis structure on a Lie algebroid


Presenting author: Paulo Antunes and Joana Nunes da Costa


Pseudo-Poisson Nijenhuis structures on Lie algebroids were recently introduced in [Na].
We investigate the relationship between pseudo-Poisson Nijenhuis structures on a Lie algebroid $ A$ and already known structures. Namely, we consider exact Poisson quasi-Nijenhuis structures and hypersymplectic structures with torsion on a Lie algebroid $ A$ [HST], and generalized complex structures on a certain Courant algebroid structure on $ A\oplus A^*$ [HS].

[HS] P. Antunes, J. M. Nunes da Costa, Hypersymplectic structures on Courant algebroids, J. Geom. Mechanics 7 (2015) 255-280.
[HST] P. Antunes, J. M. Nunes da Costa, Hypersymplectic structures with torsion on Lie algebroids, J. Geom. Phys. 104 (2016) 39-53.
[Na] T. Nakamura, Pseudo-Poisson Nijenhuis manifolds, arXiv:1703.09408.