Cosymplectic-Nijenhuis structures on Lie groupoids. (English) Zbl 1359.53065
Grabowska, Katarzyna (ed.) et al., Geometry of jets and fields. Selected papers based on the presentations at the workshop, Będlewo, Poland, May 10–16, 2015. In honour of Professor Janusz Grabowski on the occasion of his 60th birthday. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-34-8/pbk). Banach Center Publications 110, 295-307 (2016).
Summary: This paper introduces cosymplectic-Nijenhuis structures on smooth manifolds and proposes alternative odd-dimensional counterparts of symplectic-Nijenhuis groupoids, called cosymplectic-Nijenhuis groupoids. We discuss the correspondence between cosymplectic groupoids and integrable coPoisson manifolds. Moreover, we investigate the integrability problem for coPoisson manifolds equipped with a compatible Nijenhuis operator. As a result, we obtain a one-to-one correspondence between cosymplectic-Nijenhuis groupoids and integrable coPoisson-Nijenhuis manifolds.
For the entire collection see [Zbl 1359.53004].
For the entire collection see [Zbl 1359.53004].
MSC:
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
| 17B63 | Poisson algebras |
| 57R17 | Symplectic and contact topology in high or arbitrary dimension |
References:
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