Transformation to pseudo-Cartesian coordinates in locally flat pseudo-Riemannian spaces

DOI10.1016/j.geomphys.2006.12.001zbMath1117.53016OpenAlexW1974574105WikidataQ115353434 ScholiaQ115353434MaRDI QIDQ886333

Joshua T. Horwood, Raymond G. Mclenaghan

Publication date: 26 June 2007

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2006.12.001

zbMATH Keywords

curvilinear coordinatesHamilton-Jacobi theoryseparation of variablesflat pseudo-Riemannian spacesparallel covector fields

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Hamilton-Jacobi equations in mechanics (70H20) Applications of local differential geometry to the sciences (53B50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (4)

Classification of the orthogonal separable webs for the Hamilton-Jacobi and Klein-Gordon equations on 3-dimensional Minkowski space ⋮ Orthogonal separation of variables for the Hamilton-Jacobi and wave equations in three-dimensional Minkowski space ⋮ Orthogonal separation of the Hamilton-Jacobi equation on spaces of constant curvature ⋮ The classical Bertrand-Darboux problem

Cites Work

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• Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
• Separable systems of Stäckel
• Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
• Group invariant classification of separable Hamiltonian systems in the Euclidean plane and the O(4)-symmetric Yang–Mills theories of Yatsun
• An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics
• 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
• A geometrical approach to the problem of integrability of Hamiltonian systems by separation of variables

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