A general method to construct invariant PDEs on homogeneous manifolds

Let [Formula: see text] be an text]-dimensional homogeneous manifold and the of text]-jets hypersurfaces text]. The Lie group acts naturally on each A text]-invariant partial differential equation order for (i.e., with independent variables dependent one) is defined as a hypersurface We describe general method constructing such invariant equations problem reduces to description hypersurfaces, in certain vector space, which are respect linear action stability subgroup text]-prolonged apply this approach Euclidean space conformal Our works under some mild assumptions text], namely: A1) must have open orbit A2) stabilizer fiber factorize via translations itself.