Lax pair tensors and integrable spacetimes
نویسنده
چکیده
The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a wellknown Lax representation – the three-particle open Toda lattice – is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certain Riemannian geometry. By using different canonical transformations we obtain two inequivalent geometries which both represent the original system. Adding a timelike dimension gives four-dimensional spacetimes which admit two Killing vector fields and are completely integrable.
منابع مشابه
Geometrization of the Lax Pair Tensors
The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan’s torsion tensor. Three dimensional spacetimes admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.
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