An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics

DOI10.1063/1.1644902zbMath1070.37036OpenAlexW2095187878WikidataQ115334016 ScholiaQ115334016MaRDI QIDQ4833348

Dennis The, Roman G. Smirnov, Raymond G. Mclenaghan

Publication date: 15 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1644902

Mathematics Subject Classification ID

Related Items (20)

Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space ⋮ Classification of the orthogonal separable webs for the Hamilton-Jacobi and Klein-Gordon equations on 3-dimensional Minkowski space ⋮ Equivalence problem for the orthogonal separable webs in 3-dimensional hyperbolic space ⋮ Geometrical classification of Killing tensors on bidimensional flat manifolds ⋮ A class of superintegrable systems of Calogero type ⋮ Transformation to pseudo-Cartesian coordinates in locally flat pseudo-Riemannian spaces ⋮ Integrable quintic polynomial potential and its generalizations ⋮ Orthogonal separation of variables for the Hamilton-Jacobi and wave equations in three-dimensional Minkowski space ⋮ The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature ⋮ Orthogonal separation of the Hamilton-Jacobi equation on spaces of constant curvature ⋮ The classical Bertrand-Darboux problem ⋮ Covariants, joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature ⋮ Recursive moving frames ⋮ On the theory of algebraic invariants of vector spaces of Killing tensors ⋮ Killing tensors as irreducible representations of the general linear group ⋮ Recursive moving frames for Lie pseudo-groups ⋮ Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta ⋮ Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics ⋮ The 1856 lemma of Cayley revisited. I. Infinitesimal generators ⋮ Equivalence problem for the orthogonal webs on the 3-sphere

Cites Work

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• Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
• Killing tensors in spaces of constant curvature
• Killing Tensors and Variable Separation for Hamilton-Jacobi and Helmholtz Equations
• Lax representation, r-matrix method, and separation of variables for the Neumann-type restricted flow
• Superintegrable n=2 systems, quadratic constants of motion, and potentials of Drach
• Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
• TRI–HAMILTONIAN VECTOR FIELDS, SPECTRAL CURVES AND SEPARATION COORDINATES
• Theory of separability of multi-Hamiltonian chains
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• On the Separation of Variables for the Laplace Equation $\Delta \psi + K^2 \psi = 0$ in Two- and Three-Dimensional Minkowski Space
• Intrinsic Characterizations of Orthogonal Separability for Natural Hamiltonians with Scalar Potentials on Pseudo-Riemannian Spaces
• The Fundamental Theorem on Quadratic First Integrals
• A geometrical approach to the problem of integrability of Hamiltonian systems by separation of variables

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