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

摘要

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.