On some categories of Monge-Ampère systems of equations

The paper looks at differential-geometric structures associated with Monge-Ampère systems of equations on manifolds and how they can be applied in the reduction of these equations. The category of Monge-Ampère systems of equations is investigated; its morphisms are changes of independent and dependent variables. Some subcategories of this category are also studied. The main emphasis is on subcategories of equations of locally equivalent triangular and semitriangular systems, systems that are linear with respect to derivatives (semilinear systems), systems with constant coefficients, and also complete differential systems. Tests, which can be verified effectively, are proved; these make it possible to establish whether a given system of Monge-Ampère equations belongs to the subcategories listed above. As corollaries, conditions for a Monge-Ampère system to be locally reducible to a single first- or second-order equation are obtained.
Bibliography: 14 titles.