Killing Tensors with Nonvanishing Haantjes Torsion and Integrable Systems

    2015, Volume 20, Number 4, pp.  463-475

    Author(s): Tsiganov A. V.

    The second-order integrable Killing tensor with simple eigenvalues and vanishing Haantjes torsion is the key ingredient in construction of Liouville integrable systems of St├Ąckel type. We present two examples of the integrable systems on three-dimensional Euclidean space associated with the second-order Killing tensors possessing nontrivial torsion. Integrals of motion for these integrable systems are the second- and fourth-order polynomials in momenta, which are constructed using a special family of the Killing tensors.
    Keywords: Killing tensors, integrable systems, separation of variables
    Citation: Tsiganov A. V., Killing Tensors with Nonvanishing Haantjes Torsion and Integrable Systems, Regular and Chaotic Dynamics, 2015, Volume 20, Number 4, pp. 463-475



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