Exact solution of Dirac and Klein-Gordon-Fock equations in a curved space admitting a second Dirac operator

We give a brief review of integration methods of relativistic wave equations in curved spaces. On the basis of a non-commutative integration method we give an exact solution of Dirac and Klein-Gordon-Fock equations in a four-dimensional Ricci flat manifold admitting a second Dirac operator. Some analytical properties of the solutions are studied. We compare spectra of spin and scalar particles as well. A visual model of the supersymmetry structure which arises is considered and the physical sense of the second Dirac operator is explained.