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

2004/07/31 by Roman G. Smirnov, Jin Yue · 18 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Constant (computer programming) #Constant curvature #Curvature #Elasticity and Material Modeling #Equivalence (formal languages) #Euclidean geometry #Geometry #Invariant (physics) #Killing vector field #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Nonlinear Waves and Solitons #Pure mathematics #math-ph #math.MP #msc:13A50 #msc:53B21 #msc:58J70

paper · pdf · doi:10.1063/1.1805728

published in Journal of Mathematical Physics 45(11), 4141-4163 (American Institute of Physics) · 60 pages. to appear in J. Math. Phys

arxiv created 2004/08/03 · openalex publication_date 2004/10/23 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 nontrivial Killing tensors of valence two defined in the Euclidean and Minkowski planes. Illustrative examples are provided.

Citations

• Moving Coframes: II. Regularization and Theoretical Foundations
• Moving Coframes: I. A Practical Algorithm
• On Cartan’s method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry
• The 1856 Lemma of Cayley Revisited
• The moving frame, differential invariants and rigidity theorems for curves in homogeneous spaces
• A Simple Way of Making a Hamiltonian System Into a Bi-Hamiltonian One
• Killing tensors in spaces of constant curvature