Geodesic
A Lie-Algebraic Formulation for Triply Orthogonal and General Coordinate Systems in Three-Dimensional Euclidean and Lorentz Spaces
Journal of Lie theory, Tome 24 (2014) no. 2, pp. 397-419

Voir la notice de l'article provenant de la source Heldermann Verlag

We give a Lie-algebraic formulation for the interacting geometries of orthogonal families of coordinate surfaces in 3-dimensional Euclidean- and Lorentz-orthogonal coordinate systems. A study of the Gauss-Lam� equations and their variational equations in this setting leads to formulas for constructing more general 3-dimensional coordinate transformations. To motivate the general constructions, we begin with special cases of orthogonal coordinate systems in 3-dimensional Lorentz space, built from orthogonal systems in the plane.
Classification : 53C21, 53C12, 53A05, 53A35, 53Z05
Mots-clés : Orthogonal coordinate systems, Gauss-Lame equations, Lorentz space 
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     title = {A {Lie-Algebraic} {Formulation} for {Triply} {Orthogonal} and {General} {Coordinate} {Systems} in {Three-Dimensional} {Euclidean} and {Lorentz} {Spaces}},
     journal = {Journal of Lie theory},
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B. A. Shipman; P. D. Shipman . A Lie-Algebraic Formulation for Triply Orthogonal and General Coordinate Systems in Three-Dimensional Euclidean and Lorentz Spaces. Journal of Lie theory, Tome 24 (2014) no. 2, pp. 397-419. http://geodesic.mathdoc.fr/item/JLT_2014_24_2_JLT_2014_24_2_a4/