The classification of Lagrangian bundles over surfaces
type: Item
instance of: scholarly article
title: The classification of Lagrangian bundles over surfaces
zbMATH Open document ID: 0921.58018
DOI: 10.1016/S0926-2245(96)00024-1
author: K. N. Mishachev
published in: Differential Geometry and its Applications
publication date: 1999-09-26T00:00:00Z
review text: The author gives two classifications of Lagrangian bundles up to fiberwise symplectomorphism. The first classification is for Lagrangian bundles with fiber \({\mathbb R}^n\) and the second classification is for Lagrangian bundles with compact fiber, that is the 2-torus \({\mathbb T}^2\), over orientable closed surfaces. For this last classification, the author establishes a classification of complete closed lattices on the 2-torus. Some conjectures and open questions are discussed.
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1019164
zbMATH Keywords: Lagrangian bundle
zbMATH Keywords: lattice on a manifold
zbMATH Keywords: Liouville-Arnold theorem
zbMATH Keywords: global action-angle coordinates
zbMATH Keywords: fiberwise symplectomorphism
zbMATH Keywords: compact fibre
zbMATH Keywords: 2-torus
Wikidata QID: Q115337664
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
cites work: Q3361489
cites work: Q4275429
cites work: Q3961493
cites work: On global action-angle coordinates
cites work: New Invariants of Open Symplectic and Contact Manifolds
cites work: Q4711785
cites work: Affine manifolds with nilpotent holonomy
cites work: Symplectic structures on \(T^ 2\)-bundles over \(T^ 2\)
cites work: On the existence of a connection with curvature zero
cites work: Classification of \(T^ 2-bundles\) over \(T^ 2\)
cites work: Rigidité symplectique dans le cotangent de \(T^ n\). (Symplectic rigidity on the cotangent bundle of \(T^ n)\)
cites work: Shorter Notes: Some Simple Examples of Symplectic Manifolds
full work available at URL: s0926-2245(96)00024-1
OpenAlex ID: W1969506193
description: scientific article; zbMATH DE number 1019164