| In this dissertation, we investigate some questions about the deformation theory of bihamiltonian structures of hydrodynamic type. The simplest example of such a structure is that of the dispersionless KdV hierarchy. For this particular bihamiltonian structure 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 ∂ u of the field is inverted. We reformulate the original question about deformations as a question about the cohomology of a certain double complex. We then calculate the appropriate cohomology group. |
