Cosymplectic-Nijenhuis structures on Lie groupoids
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.