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The foundation: the algebraic integrability conditions

In: An Algebraic Geometric Approach to Separation of Variables

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  • Konrad Schöbel

    (Friedrich-Schiller-Universität Jena)

Abstract

In this chapter we translate the Nijenhuis integrability conditions for a Killing tensor on a constant curvature manifold into algebraic conditions on the corresponding algebraic curvature tensors. To this end, we substitute (0.7) into (0.2) and both into (0.3) and then use the representation theory for general linear groups to get rid of the dependence on the base point in the manifold.

Suggested Citation

  • Konrad Schöbel, 2015. "The foundation: the algebraic integrability conditions," Springer Books, in: An Algebraic Geometric Approach to Separation of Variables, chapter 1, pages 25-54, Springer.
    • Handle: RePEc:spr:sprchp:978-3-658-11408-4_2
    DOI: 10.1007/978-3-658-11408-4_2
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