摘要: The use of Lax pair tensors as a unifying framework for Killing arbitrary rank is discussed. Some properties the tensorial formulation are stated. A mechanical system with well-known representation—the three-particle open Toda lattice—is geometrized by suitable canonical transformation. In this way lattice realized geodesic certain Riemannian geometry. By using different transformations we obtain two inequivalent geometries which both represent original system. Adding timelike dimension gives four-dimensional spacetimes admit vector fields and completely integrable.
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