Introduction to Symplectic Geometry

DOI10.1007/978-981-13-3987-5zbMath1433.53002OpenAlexW2939254726MaRDI QIDQ4623456

Yi Ming Zou, Jean-Louis Koszul

Publication date: 15 February 2019

Full work available at URL: https://doi.org/10.1007/978-981-13-3987-5

zbMATH Keywords

symplectic manifoldsPoisson manifoldsinformation geometrysupermanifoldsmoment mapsFisher metric

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Poisson manifolds; Poisson groupoids and algebroids (53D17) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry (53-01) Natural bundles (58A32) Information geometry (statistical aspects) (62B11)

Related Items (11)

Polysymplectic Souriau Lie group thermodynamics and the geometric structure of its coadjoint orbits ⋮ Polysymplectic Souriau Lie group thermodynamics and entropy geometric structure as Casimir invariant function ⋮ Poisson geometry of the statistical Frobenius manifold ⋮ Symplectic scalar curvature on the supermanifold of differential forms ⋮ Invariant Koszul Form of Homogeneous Bounded Domains and Information Geometry Structures ⋮ Special issue ``Affine differential geometry and Hesse geometry: a tribute and memorial to Jean-Louis Koszul ⋮ Koszul lecture related to geometric and analytic mechanics, Souriau's Lie group thermodynamics and information geometry ⋮ Jean-Louis Koszul and the Elementary Structures of Information Geometry ⋮ Jean-Marie Souriau’s Symplectic Model of Statistical Physics: Seminal Papers on Lie Groups Thermodynamics - Quod Erat Demonstrandum ⋮ Souriau-Casimir Lie Groups Thermodynamics and Machine Learning ⋮ Archetypal model of entropy by Poisson cohomology as invariant Casimir function in coadjoint representation and geometric Fourier heat equation

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