Lax pair tensors in arbitrary dimensions
  A recipe is presented for obtaining Lax tensors for any n-dimensional Hamiltonian system admitting a Lax representation of dimension n. Our approach is to use the Jacobi geometry and coupling-constant metamorphosis to obtain a geometric Lax formulation. We also exploit the results to construct integrable spacetimes, satisfying the weak energy condition. 
Martin Goliath, Max Karlovini, and Kjell Rosquist