Absolute Equivalence of Exterior Differential Systems

摘要

This paper concerns an equivalence relation first defined by E. Cartan for certain systems of ordinary differential equations. He called two systems absolutely equivalent if they had isomorphic prolongations. The author extends Cartan's definition to general exterior differential systems. Two exterior differential systems are absolutely equivalent if there exists a sequence of systems beginning with one and ending with the second in which for each adjacent pair one is a partial prolongation of its neighbor. Two kinds of numerical invariants are found, depending on the characters s sub o, s sub 1, . . ., s sub p. Using Kuranishi's infinite analytic mappings, the last non-zero integer among s sub o, s sub 1, . . . s sub p is an absolute invariant. Other absolute invariants are computed from the sequence of prolongations of a given system.