Natural connections for semi-Hamiltonian systems: The case of the $ε$-system

Details Natural connections for semi-Hamiltonian systems: The case of the $ε$-system Natural connections for semi-Hamiltonian systems: The case of the $ε$-system

2009-12-18

arxiv.org/abs/0912.3697v3

Letters in Mathematical Physics: Volume 97, Issue 1 (2011), 85-108

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages

Scientific paper

10.1007/s11005-011-0469-x

Given a semi-Hamiltonian system, we construct an $F$-manifold with a
connection satisfying a suitable compatibility condition with the product. We
exemplify this procedure in the case of the so-called $\epsilon$-system. The
corresponding connection turns out to be flat, and the flat coordinates give
rise to additional chains of commuting flows

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