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

Abstract

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.

60 pages. to appear in J. Math. Phys

References in corpus (3)

• A simple way of making a Hamiltonian system into a bi-Hamiltonian one
• Separability in Riemannian Manifolds
• The 1856 Lemma of Cayley Revisited

Cited by in corpus (5)

• Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
• Geometrical classification of Killing tensors on bidimensional flat manifolds
• Equivalence problem for the orthogonal webs on the sphere
• A Geometric Study of Superintegrable Systems
• Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space