On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type

Details On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type

2006-02-27

arxiv.org/abs/math/0602596v1

Mathematics

Differential Geometry

24 pages

Scientific paper

We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivative of the field is inverted. We reformulate the question about deformations as a question about the cohomology of a certain double complex, and calculate the appropriate cohomology group.

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