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arXiv · 1304.4102

Hyperstructures on Lie algebroids

P. Antunes·J. M. Nunes da Costa
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Abstract

We define hypersymplectic structures on Lie algebroids recovering, as particular cases, all the classical results and examples of hypersymplectic structures on manifolds. We prove a 1-1 correspondence theorem between hypersymplectic structures and (pseudo-)hyperk\"{a}hler structures. We show that the hypersymplectic framework is very rich in already known compatible pairs of tensors such as Poisson-Nijenhuis, $\Omega N$ and $P \Omega$ structures.

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P. Antunes, J. M. Nunes da Costa. 2013-04-15. Hyperstructures on Lie algebroids. https://doi.org/10.1142/s0129055x13430034

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