LAX PAIR TENSORS AND INTEGRABLE SPACETIMES

The use of Lax pair tensors as a unifying framework for Killing tensor s of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a well-known La x representation - the three-particle open Toda lattice - is geometriz ed by a suitable canonical transformation. In this way the Toda lattic e is realized as the geodesic system of a certain Riemannian geometry. By using different canonical transformations we obtain two inequivale nt geometries which both represent the original system. Adding a timel ike dimension gives four-dimensional spacetimes which admit two Killin g vector fields and are completely integrable.