Hyper-symplectic structures on integrable systems

Abstract

We prove that an integrable system over a symplectic manifold, whose symplectic form is covariantly constant w.r.t. the Gauss-Manin connection, carries a natural hyper-symplectic structure. Moreover, a special Kaehler structure is induced on the base manifold.

LaTeX file, 7 pages; to be published in Journal of Geometry and Physics

References in corpus (5)

• Supersymmetric Yang-Mills Systems And Integrable Systems
• Special Kahler Manifolds
• Special complex manifolds
• Fukaya category and Fourier transform
• A Fourier transform for sheaves on Lagrangian families of real tori

Cited by in corpus (6)

• Special symplectic Lie groups and hypersymplectic Lie groups
• Metric geometries over the split quaternions
• Explicit Quaternionic Contact Structures and Metrics with Special Holonomy
• Hypersymplectic manifolds and associated geometries
• Bianchi type A hyper-symplectic and hyper-Kähler metrics in 4D
• Some remarks on special Kähler geometry