On the completeness of the Manakov integrals

Abstract

The aim of this note is to present simple proofs of the completeness of Manakov's integrals for a motion of a rigid body fixed at a point in ${\mathbb{R}}^n$, as well as for geodesic flows on a class of homogeneous spaces $SO(n)/SO(n_1)\times \cdots \times SO(n_r)$.

11 pages, 1 figure, an extended version of the note will appear in: Fundamentalnaya i Prikladnaya Matematika (in Russian); Journal of Mathematical Sciences (in English)

References in corpus (1)

• Integrability of Invariant Geodesic Flows on n-Symmetric Spaces