Connections of Berry and Hannay type for moving Lagrangian submanifolds

DOI10.1016/0001-8708(90)90086-3zbMath0713.58015OpenAlexW2024314715MaRDI QIDQ749946

Alan Weinstein

Publication date: 1990

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(90)90086-3

zbMATH Keywords

Lagrangian submanifoldsBerry connectionHannay connection

Mathematics Subject Classification ID

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

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Cites Work

• The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case
• The local structure of Poisson manifolds
• Lagrangian submanifolds and Hamiltonian systems
• Cohomology of symplectomorphism groups and critical values of Hamiltonians
• Reduction of symplectic manifolds with symmetry
• Symplectic manifolds and their Lagrangian submanifolds
• ANALOGUES OF THE OBJECTS OF LIE GROUP THEORY FOR NONLINEAR POISSON BRACKETS
• Quantal phase factors accompanying adiabatic changes
• Classical adiabatic angles and quantal adiabatic phase
• Classical non-adiabatic angles
• Symplectic groupoids and Poisson manifolds
• Convexity and Tightness for Restrictions of Hamiltonian Functions to Fixed Point Sets of an Antisymplectic Involution
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