Abstract
A canonical correspondence between Hamiltonian systems of differential equations of hydrodynamic type and hypersurfaces of a pseudo-Euclidean space is constructed. In this correspondence multi-Hamiltonian systems correspond to hypersurfaces admitting nontrivial deformations that preserve the principal directions and principal curvatures. A description of the surfaces inE 3 that admit a three-parameter family of such deformations is given.
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Translated fromItogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 22, 1990, pp. 59–96.
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Ferapontov, E.V. Hamiltonian systems of hydrodynamic type and their realization on hypersurfaces of a pseudo-Euclidean space. J Math Sci 55, 1970–1995 (1991). https://doi.org/10.1007/BF01095672
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DOI: https://doi.org/10.1007/BF01095672