Veronese webs for bihamiltonian structures of higher corank

Abstract

It is shown how the well-known class of bihamiltonian structures in general position can be extended to a wider class. A generalization of the corresponding notion of a Veronese web for this wider class is presented (in the general position case Veronese webs form complete systems of local invariants for bihamiltonian structures). Some examples are considered.

11p. To appear in: Banach Center Publications, Proc. of "Poisson Geometry" conference dedicated to the memory of Stanislaw Zakrzewski, Warsaw 1998, J.Grabowski, P.Urbanski eds

References in corpus (2)

• Webs, Lenard schemes, and the local geometry of bihamiltonian Toda and Lax structures
• Kronecker webs, bihamiltonian structures, and the method of argument translation

Cited by in corpus (10)

• On a Poisson reduction for Gel'fand--Zakharevich manifolds
• On integrability of generalized Veronese curves of distributions
• Projections of Jordan bi-Poisson structures that are Kronecker, diagonal actions, and the classical Gaudin systems
• On the local theory of Veronese webs
• Symplectic realizations of bihamiltonian structures
• Curvature of Poisson pencils in dimension three
• Webs and the Plebański equation
• Jordan-Kronecker invariants of finite-dimensional Lie algebras
• The Local Product Theorem for bihamiltonian structures
• Algebraic Nijenhuis operators and Kronecker Poisson pencils