Geodesic
A Lie-Algebraic Formulation for Triply Orthogonal and General Coordinate Systems in Three-Dimensional Euclidean and Lorentz Spaces
Barbara A. Shipman1 ; Patrick D. Shipman2
1Dept. of Mathematics, University of Texas, Box 19408, Arlington, TX 76019, U.S.A.
2Dept. of Mathematics, Colorado State University, Box 1874, Fort Collins, CO 80523, U.S.A.
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-Lamé 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

Barbara A. Shipman  1   ; Patrick D. Shipman  2

1 Dept. of Mathematics, University of Texas, Box 19408, Arlington, TX 76019, U.S.A.
2 Dept. of Mathematics, Colorado State University, Box 1874, Fort Collins, CO 80523, U.S.A. 
Barbara A. Shipman; Patrick 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/JOLT_2014_24_2_a4/
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     author = {Barbara A. Shipman and Patrick D. Shipman},
     title = {A {Lie-Algebraic} {Formulation} for {Triply} {Orthogonal} and {General} {Coordinate} {Systems} in {Three-Dimensional} {Euclidean} and {Lorentz} {Spaces}},
     journal = {Journal of Lie Theory},
     pages = {397--419},
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