Stationary points on the doublet and quartet hypersurfaces of the N-3 system are studied using the single-configurational and multi-configurational Hartree-Fock approaches and the methods which include the dynamic correlation effects on a perturbational way or through the density functional theory (DFT). A general structure of both the hypersurfaces within the C-2 upsilon symmetry is explained on the basis of the Walsh diagram and studied by a simplified configuration interaction (CI) based on a small complete active space (CAS) of five valence orbitals. The minima found in this way are studied in detail by the other methods mentioned above without the symmetry constraints. The stability of minima and existence of energetic barriers are explained by the changes of the bonding - antibonding character of some valence orbitals, observed in the Walsh diagrams for both the orbital and the Kohn-Sham energies. All the methods applied indicate, that a stable ring N-3 conformer should exist with the B-2(1) ground state. Alternative mechanisms for a deactivation of the linear excited states of N-3 are proposed.