The geometry of a bi-Lagrangian manifold
type: Item
instance of: scholarly article
title: The geometry of a bi-Lagrangian manifold
zbMATH Open document ID: 1101.53047
author: Rafael Santamaría
author: Ujué R. Trías
author: Fernando Etayo
published in: Differential Geometry and its Applications
publication date: 2006-05-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0403512
review text: In this survey the authors study bi-Lagrangian manifolds. Bi-Lagrangian manifolds are symplectic manifolds with two transversal Lagrangian foliations. The authors also consider the case when the two transversal Lagrangian distributions are non-integrable. They show that many different geometric structures can be attached to these manifolds and they analyze the associated connections. They introduce the problem of the intersection of the two leaves of the foliations.
reviewed by: Wojciech Domitrz
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 5028924
zbMATH Keywords: symplectic
zbMATH Keywords: bi-Lagrangian
zbMATH Keywords: connection
zbMATH Keywords: foliation
zbMATH Keywords: para-Kähler
MaRDI profile type: Publication
OpenAlex ID: W2054369882
Wikidata QID: Q115357932
arXiv ID: math/0403512
cites work: Q4174811
cites work: Special complex manifolds
cites work: Métriques Kählériennes Affinement Plates De Certaines Variétés Symplectiques I
cites work: Lectures on symplectic geometry
cites work: Q4507806
cites work: Generalised connections over a vector bundle map.
cites work: Riemannian geometry of Lagrangian submanifolds
cites work: Manifolds with holonomy group \(Z_2\oplus Z_2\) and first Betti number zero
cites work: Q3658695
cites work: Q4539697
cites work: A survey on paracomplex geometry
cites work: Isospectral compact flat manifolds
cites work: Q4764808
cites work: Q4291419
cites work: Q4498304
cites work: Q4882723
cites work: The measure of holomorphicness of a real submanifold of an almost Hermitian manifold
cites work: Q4883961
cites work: Q5705790
cites work: \((J^2=\pm 1)\)-metric manifolds
cites work: The canonical connection of a bi-Lagrangian manifold
cites work: Q3535181
cites work: A simple geometrical construction of deformation quantization
cites work: The invariant connection of a \({1\over 2}\)-pinched Anosov diffeomorphism and rigidity
cites work: Lie algebroids, holonomy and characteristic classes
cites work: Q3879899
cites work: Spaces of constant para-holomorphic sectional curvature
cites work: Q4274239
cites work: The paracomplex projective spaces as symmetric and natural spaces
cites work: Q4850982
cites work: Riemannian geometry
cites work: Osserman manifolds in semi-Riemannian geometry
cites work: Nonsymmetric Osserman pseudo-Riemannian manifolds
cites work: Fedosov manifolds
cites work: Q4195061
cites work: Q4143433
cites work: Q3915678
cites work: Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations
cites work: Paracomplex structures and affine symmetric spaces
cites work: Q5731354
cites work: Sur le problème d'équivalence de certaines structures infinitésimales
cites work: Q3313005
cites work: Three-manifolds admitting metrics with the same geodesics
cites work: Q5461285
cites work: Q4374336
cites work: Q3312869
cites work: Q5019699
cites work: Compact flat manifolds with holonomy group 𝐙₂⊕𝐙₂
cites work: Q4719108
cites work: Bi-Hamiltonian systems and Maslov indices
cites work: A canonical connection associated with certain G-structures
cites work: Almost Tangent and Cotangent Structures in the Large
cites work: Foliations on Riemannian manifolds

The geometry of a bi-Lagrangian manifold (cites work)
cites work: Basics of Lagrangian foliations

The geometry of a bi-Lagrangian manifold (cites work)
cites work: Q5678143

The geometry of a bi-Lagrangian manifold (DOI)
DOI: 10.1016/J.DIFGEO.2005.07.002