On the Darboux–Nijenhuis variables on the Poisson manifold $so^*(4)$

A. V. Vershilov, A. V. Tsiganov

Saint-Petersburg State University

Abstract: We classify quadratic Poisson structures on $so^*(4)$ and $e^*(3)$, which have the same foliations by symplectic leaves as canonical Lie-Poisson tensors. The separated variables for some of the corresponding bi-integrable systems are constructed.

Keywords: integrable system, bi-hamiltonian geometry, separation of variables.

UDC: 532.5

MSC: 70H20, 70H06, 37K10