关于流体力学型双哈密顿族形变的模空间
On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type
摘要：
本文研究了最简单的流体力学型双哈密顿结构的变形理论，即无色散KdV族的变形理论。我们证明了它的所有变形在B意义下都是拟平凡的。Dubrovin和Y.也就是说，在允许场的一阶偏导数反转的变换后，它是平凡的。我们将形变问题转化为关于某个二重复形的上同调问题，并计算出相应的上同调群。
英文摘要：
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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