On geometry of second-order parabolic equations in two independent variables

Some new results concerning second order differential parabolic equation in two independent variables are presented. Equations of Monge-Ampére type are distinguished among them. The structure of these subsidiary equations allow to subdivide the parabolic equations into four classes, and each of them can be described as a special geometrical structure on 4-dimensional manifolds. The paper has three types of equations that are distinguished from one another by the character of singularities that their multi-valued solutions admit, which are described by subsidiary equations. The interpretations of the study has a number of other applications to the theory of PMA equations.