Differential Invariants of Point and Dual Transformations

Abstract

In this first Part we shall show that we can determine a complete system of differential invariants of the first order, relative to a pair of differential elements homologous in a point or dual correspondence, between portions of two Euclidean spaces, which is biregular and of class C¹.From such metric invariants will be deduced certain topological invariants relative to the united points of correspondences between superimposed varieties, as well as some projective invariants belonging to a pair of elements common to two dual correspondences, and also to two hypersurfaces of a hyperspace which touch at a common point. A deeper study of the above invariants will appear in the following two Parts.