Geometry of bi-Hamiltonian systems
type: Item
instance of: scholarly article
title: Geometry of bi-Hamiltonian systems
zbMATH Open document ID: 0793.58015
DOI: 10.1016/0019-3577(93)90002-G
author: Robert Brouzet
author: Pierre Molino
author: Francisco-Javier Turiel
published in: Indagationes Mathematicae. New Series
publication date: 1994-08-21T00:00:00Z
review text: It is well known that the various notions of compatibility between geometrical structures play a very important role in differential geometry. For instance, the compatibility between complex structures and Riemannian structures lead us naturally to the Kähler geometry. The compatibility between Riemannian structures and foliated structures determines the study of Riemannian foliations and so on. In the paper under review the authors prove that the compatibility of two symplectic structures gives rise to a very rich geometry which contains as particular cases some old results due to Darboux and Lie. The material is organized as follows. In \S1 are described the nondegenerate bi-Hamiltonian mechanical systems which are situated in a neighborhood of an invariant torus. The bi-Lagrangian fibrations make the object of the following two sections. Finally in the last section all the above results are exemplified in the particular case of a 4-dimensional compact manifold, connected and without boundary.
reviewed by: Mircea Puta
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 510026
zbMATH Keywords: bi-Hamiltonian mechanical systems
zbMATH Keywords: bi-Lagrangian fibration
zbMATH Keywords: compatibility
MaRDI profile type: Publication
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full work available at URL: 0019-3577(93)90002-g
OpenAlex ID: W1966258852
description: scientific article; zbMATH DE number 510026