Integrable systems, Poisson pencils, and hyperelliptic Lax pairs

A new Lax pair for the multidimensional Manakov system on the Lie algebra $\mathrm{so}(m)$ with a spectral parameter defined on a certain unramified covering of a hyperelliptic curve is considered. For the Clebsh–Perelomov system on the Lie algebra $e(n)$, similar pairs are presented. Multidimensional analogs of the classical integrable Steklov–Lyapunov system describing a motion of a rigid body in an ideal fluid are found. Bibl. 15 titles.