On the Local Geometry of a Bihamiltonian Structure
We give several examples of bihamiltonian manifolds and show that under very mild assumptions a bihamiltonian structure in “general position” is locally of one of these types. This shows, in particular, that a bihamiltonian manifold in general position is always a moduli space of some kind. In the even-dimensional case it is a Hubert scheme of a surface, in the odd-dimensional case it is a sub- cotangent bundle of a moduli space of rational curves on a surface.
KeywordsFiltration Manifold Soliton Intersection Line Allo
Unable to display preview. Download preview PDF.
- 3.Israel M. Gelfand and Ilya Zakharevich, The spectral theory for a pencil of skew-symmetrical differential operators of third order, preprint MSRI-06627-91, MSRI, Berkeley, CA, 94720, 1991.Google Scholar
- 4.Alexander Goncharov, private communication, 1990.Google Scholar
- 5.Kunihiko Kodaira, Complex manifolds and deformation of complex structures, Grundlehren der mathematischen Wissenschaften, vol. 283, Springer-Verlag, New York, 1986.Google Scholar
- 6.F. Magri, Geometry and soliton equations, La Mécanique Analytique de Lagrange et son héritage, Collège de France, September 1988.Google Scholar
- 7.Henri McKean, private communication, 1990.Google Scholar