Displaying similar documents to “An integrable flow on a family of Hilbert Grassmannians.”

Transverse Hilbert schemes and completely integrable systems

Niccolò Lora Lamia Donin (2017)

Complex Manifolds


In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial...

Lagrange functions generating Poisson manifolds of geodesic arcs

Klapka, Lubomír


Let X a smooth finite-dimensional manifold and W Γ ( X ) the manifold of geodesic arcs of a symmetric linear connection Γ on X . In a previous paper [Differential Geometry and Applications (Brno, 1995) 603-610 (1996; Zbl 0859.58011)] the author introduces and studies the Poisson manifolds of geodesic arcs, i.e. manifolds of geodesic arcs equipped with certain Poisson structure. In this paper the author obtains necessary and sufficient conditions for that a given Lagrange function generates a...