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The invariant theory of Killing tensors (ITKT) is extended by introducing thenew concepts of covariants and joint invariants of (product) vector spaces ofKilling tensors defined in pseudo-Riemannian spaces of constant curvature. Thecovariants are employed to solve the problem of classification of theorthogonal coordinate webs generated by non-trivial Killing tensors of valencetwo defined in the Euclidean and Minkowski planes. Illustrative examples areprovided.Comment: 60 pages. to appear in J. Math. Phy

journal of mathematical physics

Covariants, joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature