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24 April 2024 |
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First integrals of affine connections and Hamiltonian systems of hydrodynamic type | | Felipe Contatto
; Maciej Dunajski
; | | Date: |
7 Oct 2015 | | Abstract: | We find necessary and sufficient conditions for a local geodesic flow of an
affine connection on a surface to admit a linear first integral. The conditions
are expressed in terms of two scalar invariants of differential orders 3 and 4
in the connection. We use this result to find explicit obstructions to the
existence of a Hamiltonian formulation of Dubrovin--Novikov type for a given
one--dimensional system of hydrodynamic type. We give several examples
including Zoll connections, and Hamiltonian systems arising from
two--dimensional Frobenius manifolds | | Source: | arXiv, 1510.1906 | | Services: | Forum | Review | PDF | Favorites | |
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