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Locally conformal symplectic manifolds [PDF]

International Journal of Mathematics and Mathematical Sciences, 1985
A locally conformal symplectic (l. c. s.) manifold is a pair (M2n,Ω) where M2n(n>1) is a connected differentiable manifold, and Ω a nondegenerate 2-form on M such that M=⋃αUα (Uα- open subsets). Ω/Uα=eσαΩα, σα:Uα→ℝ, dΩα=0.
Izu Vaisman
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Entropic Dynamics Approach to Quantum Electrodynamics [PDF]

Entropy
Entropic Dynamics (ED) is a framework that allows one to derive quantum theory as a Hamilton–Killing flow on the cotangent bundle of a statistical manifold.
Ariel Caticha
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HC-SPA: Hyperbolic Cosine-Based Symplectic Phase Alignment for Fusion Optimization [PDF]

Sensors
In multimodal collaborative learning, the gradient dynamics of heterogeneous modalities face significant challenges due to the curvature heterogeneity of parameter manifolds and mismatches in phase evolution.
Wenlong Zhang, Aiqing Fang, Ying Li, Yan Wei   +3 more
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Symplectic Pairs and Intrinsically Harmonic Forms

Mathematics, 2023
In this short note, we prove two properties of symplectic pairs on a four-manifold: firstly we prove that two transversal orientable foliations of codimension two, which are taut for the same Riemannian metric, are the characteristic foliations of a ...
Gianluca Bande
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Complex Lagrangians in a hyperKähler manifold and the relative Albanese

Complex Manifolds, 2020
Let M be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold X, and let ω̄ : 𝒜̂ → M be the relative Albanese over M. We prove that 𝒜̂ has a natural holomorphic symplectic structure.
Biswas Indranil, Gómez Tomás L., Oliveira André   +2 more
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Contact Dynamics: Legendrian and Lagrangian Submanifolds

Mathematics, 2021
We are proposing Tulczyjew’s triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These geometries permit
Oğul Esen, Manuel Lainz Valcázar, Manuel de León, Juan Carlos Marrero   +3 more
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Lagrangian Submanifolds of Symplectic Structures Induced by Divergence Functions

Entropy, 2020
Divergence functions play a relevant role in Information Geometry as they allow for the introduction of a Riemannian metric and a dual connection structure on a finite dimensional manifold of probability distributions.
Marco Favretti
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Basic Notions of Poisson and Symplectic Geometry in Local Coordinates, with Applications to Hamiltonian Systems

Universe, 2022
This work contains a brief and elementary exposition of the foundations of Poisson and symplectic geometries, with an emphasis on applications for Hamiltonian systems with second-class constraints.
Alexei A. Deriglazov
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Leaves of stacky Lie algebroids

Comptes Rendus. Mathématique, 2020
We show that the leaves of an LA-groupoid which pass through the unit manifold are, modulo a connectedness issue, Lie groupoids. We illustrate this phenomenon by considering the cotangent Lie algebroids of Poisson groupoids thus obtaining an interesting ...
Álvarez, Daniel
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Generating functions in Symplectic Geometry

Pesquimat, 2019
In this work, we present a brief introduction to Symplectic Geometry relating its origin with the Physics. Then we present the formal definition of symplectic manifold and some important results, with this we consider a function AH;N defined in the ...
Josué Alonso Aguirre Enciso, Rodolfo José Gálvez Pérez   +1 more
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