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

Roman G. Smirnov, Jin Yue
2004 Journal of Mathematical Physics  
The invariant theory of Killing tensors (ITKT) is extended by introducing the new concepts of covariants and joint invariants of (product) vector spaces of Killing tensors defined in pseudo-Riemannian spaces of constant curvature. The covariants are employed to solve the problem of classification of the orthogonal coordinate webs generated by non-trivial Killing tensors of valence two defined in the Euclidean and Minkowski planes. Illustrative examples are provided.
doi:10.1063/1.1805728 fatcat:66uvb55d7vhh5pzoja4lhez6wi