The symmetry group of Lamé's system and the associated Guichard nets for conformally flat hypersurfaces (Q352507)

From the introduction: The Guichard nets in \(\mathbb{R}^3\) are open sets with a flat metric \(g=\sum _{i=1}^3l^2_idx^2_i\), where the coefficients \(l_i\) satisfy the Guichard condition \(l_1^2-l_2^2+l_3^2=0\), and a system of second-order partial differential equations, which is called Lamé system.NEWLINENEWLINEThe present paper obtains solutions \(l_i\) which are invariant under the actions of \(2\)-dimensional subgroups of the symmetry group of the Lamé system. There are also studied the conformally flat hypersurfaces associated to the functions \(l_i\) which are invariant under the action of translations by using a basic invariant \(\xi \).