Symmetry Group of Ţiţeica Surfaces Pde

Using the theory of the symmetry groups for PDEs of order two ([7], [17], [20]), one finds the symmetry group G associated to Ţiţeica surfaces PDE. One proves that Monge-Ampère-Ţiţeica PDE which is invariant with respect to G, where G is the maximal solvable subgroup of the symmetry group G, is just the PDE of Ţiţeica surfaces. One studies the inverse problem and one shows that the Ţiţeica surfaces PDE is an Euler-Lagrange equation. One determines the variational symmetry group of the associated functional, and one obtains the conservation laws associated to the Ţiţeica surfaces PDE. One finds some group-invariant solutions of the Ţiţeica surfaces PDE. All these results shows that Ţiţeica surfaces theory is strongly related to variational problems, and hence it is a subject of global differential geometry. Key-words: symmetry group of Ţiţeica PDE, criterion of infinitesimal invariance, inverse problem for Ţiţeica PDE, Ţiţeica Lagrangian, conservation law. Mathematics Subject Classification: 58G35, 53C99, 35A15