
Journal of Lie Theory 24 (2014), No. 2, 397419 Copyright Heldermann Verlag 2014 A LieAlgebraic Formulation for Triply Orthogonal and General Coordinate Systems in ThreeDimensional Euclidean and Lorentz Spaces Barbara A. Shipman Dept. of Mathematics, University of Texas, Box 19408, Arlington, TX 76019, U.S.A. bshipman@uta.edu Patrick D. Shipman Dept. of Mathematics, Colorado State University, Box 1874, Fort Collins, CO 80523, U.S.A. shipman@math.colostate.edu We give a Liealgebraic formulation for the interacting geometries of orthogonal families of coordinate surfaces in 3dimensional Euclidean and Lorentzorthogonal coordinate systems. A study of the GaussLamé equations and their variational equations in this setting leads to formulas for constructing more general 3dimensional coordinate transformations. To motivate the general constructions, we begin with special cases of orthogonal coordinate systems in 3dimensional Lorentz space, built from orthogonal systems in the plane. Keywords: Orthogonal coordinate systems, GaussLame equations, Lorentz space. MSC: 53C21, 53C12, 53A05, 53A35, 53Z05 [ Fulltextpdf (8132 KB)] for subscribers only. 