Differential Invariants of Point and Dual Transformations
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.
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