PARABOLIC GEOMETRIES ASSOCIATED WITH DIFFERENTIAL EQUATIONS OF FINITE TYPE
Preprint Series # 756
Yamaguchi, Keizo and Yatsui, Tomoaki PARABOLIC GEOMETRIES ASSOCIATED WITH DIFFERENTIAL EQUATIONS OF FINITE TYPE. (2005);
We present here classes of parabolic geometries arising naturally from Seashi’s principle to form good classes of linear differential equations of finite type, which generalize the cases of second and third order ODE for scalar function. We will explicitly describe the symbols of these differential equations. The model equations of these classes admit nonlinear contact transformations and their symmetry algebras (the Lie algebra of infinitesimal contact transformations preserving these equations) become finite dimensional and simple.