Abstract
It is shown that Lax equations associated with dynamical systems on T *Qof the same dimension as Q arise as local expressions of parallelism of a (1,1)-tensor field along the dynamical vector field Γ if the partial connection defined by the symplectic form Ω admissible for a Lagrangian foliation is considered.
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Carinena, J.F., Ibort, L.A. On Lax equations arising from Lagrangian foliations. Lett Math Phys 8, 21–26 (1984). https://doi.org/10.1007/BF00420037
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DOI: https://doi.org/10.1007/BF00420037