On the Local Theory of Continuous Infinite Pseudo Groups II

In this chapter, we shall formulate, without proof, the theorys of exterior differential systems and of their prolongations using the language in the theory of jets developed by C. Ehresman, because such formulation seems to be most convenient in order to apply the theory to the theory of continuous infinite pseudo-groups, which we shall discuss in the next chapter. Since important theorems in our theory hold only in the real analytic case, we shall exclusively consider the real analytic case. So, we shall omit the adjective “analytic”, unless explicitly stated otherwise. As for the fundamental notions in the theory of jets and of differential systems, we refer to [5] and [6], respectively. Detailed proof of the contents of this Chapter will be published in [7].