Basics of Lagrangian foliations
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In this article, an exposition of basic known local and global results on Lagrangian foliations such as the Theorem of Darboux-Lie, Weinstein, Arnold-Liouville, etc.Abstract:
The paper is an exposition of basic known local and global results on Lagrangian foliations such as the Theorem of Darboux-Lie, Weinstein, Arnold-Liouville, a global characterization of cotangent bundles, higher order Maslov classes, etc.read more
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Homogeneous para-Kähler Einstein manifolds
TL;DR: In this article, it was shown that any invariant para-complex structure on a semisimple Lie group defines a unique para-Kahler Einstein structure with given nonzero scalar curvature.
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The geometry of a bi-Lagrangian manifold
TL;DR: In this paper, a survey on bi-Lagrangian manifolds is presented, which are symplectic manifolds endowed with two transversal Lagrangian foliations.
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Homogeneous para-K\"ahler Einstein manifolds
TL;DR: In this paper, the authors define a para-K\"ahler manifold as a pseudo-Riemannian manifold with a parallel skew-symmetric para-complex structure.
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The canonical connection of a bi-Lagrangian manifold
F Etayo Gordejuela,R Santamaría +1 more
TL;DR: In this article, it was shown that the canonical connection of a bi-Lagrangian manifold introduced by Hess is a Levi-Civita connection, showing that such a manifold endowed with two transversal Lagrangian foliations has a canonical semi-Riemannian metric.
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Lagrangian Distributions and Connections in Symplectic Geometry
Michael Forger,Sandra Z. Yepes +1 more
TL;DR: In this paper, the interplay between lagrangian distributions and connections in symplectic geometry is discussed, beginning with the traditional case of symplectic manifolds and then passing to the more general context of poly-and multisymplectic structures on fiber bundles, which is relevant for the covariant hamiltonian formulation of classical field theory.
References
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Le Probleme General des Variables Actions-Angles
Pierre Dazord,Thomas Delzant +1 more
TL;DR: Feuilletages symplectiquement complets. Classe de Chern as discussed by the authors : Monodromie des fibrations isotropes symplectique completes. Structure locale and theoreme des variables action-angles.
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De rham homology for networks of manifolds
TL;DR: In this article, the real homology of networks is described in terms of differential forms and a generalized Thom isomorphism theorem is also proved in this context, where networks include, besides smooth manifolds, singular sets of toral actions, classifying spaces of Lie groups, etc.