Symmetry Group of Tzitzeica Surfaces PDE

Using the symmetry group theory of second order PDEs, one finds the symmetry group associated to Tzitzeica surfaces partial differential equation. One studies the inverse problem and one shows that the Tzitzeica surfaces PDE is an Euler-Lagrange equation. One determines the variational symmetry group of the associated functional and one obtains the conservation laws of the Tzitzeica surfaces PDE. All these results shows that the Tzitzeica surfaces theory is strongly related to variational problems and hence it is a subject of global differential geometry.