Deformations of the Bihamiltonian Structures on the Loop Space of Frobenius Manifolds
نویسندگان
چکیده
We consider an important class of deformations of the genus zero bihamiltonian structure defined on the loop space of semisimple Frobenius manifolds, and present results on such deformations at the genus one and genus two approximations.
منابع مشابه
Preprint SISSA 25/98/FM FLAT PENCILS OF METRICS AND FROBENIUS MANIFOLDS
s This paper is based on the author’s talk at 1997 Taniguchi Symposium “Integrable Systems and Algebraic Geometry”. We consider an approach to the theory of Frobenius manifolds based on the geometry of flat pencils of contravariant metrics. It is shown that, under certain homogeneity assumptions, these two objects are identical. The flat pencils of contravariant metrics on a manifold M appear n...
متن کاملNormal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov Witten invariants of all genera into the theory of integrable systems. The project is focused at describing normal forms of the PDEs and their local bihamiltonian structures satisfying certain simple axioms. A Frobenius manifold or its dege...
متن کاملFrobenius manifolds and central invariants for the Drinfeld–Sokolov bihamiltonian structures
The Drinfeld–Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete sets of invariants of the related bihamiltonian structures with respect to the group of Miura-type transformations. © 2008 Elsevier Inc. All rights reserved. MSC: primary 37K10; secondary 53D5
متن کاملBihamiltonian Cohomologies and Integrable Hierarchies II: the Tau Structures
Starting from a so-called flat exact semisimple bihamiltonian structures of hydrodynamic type, we arrive at a Frobenius manifold structure and a tau structure for the associated principal hierarchy. We then classify the deformations of the principal hierarchy which possess tau structures. Mathematics Subject Classification (2010). Primary 37K10; Secondary 53D45.
متن کاملDeformations of Frobenius structures on Hurwitz spaces
Deformations of Dubrovin’s Hurwitz Frobenius manifolds are constructed. The deformations depend on g(g+1)/2 complex parameters where g is the genus of the corresponding Riemann surface. In genus one, the flat metric of the deformed Frobenius manifold coincides with a metric associated with a one-parameter family of solutions to the Painlevé-VI equation with coefficients (1/8,−1/8, 1/8, 3/8) . A...
متن کامل