Ragni Piene: Envelopes and evolutes

Abstract.

In joint work with C. Riener and B. Shapiro we studied evolutes of plane real curves. In this talk I will consider envelopes of families of linear spaces over a projective complex variety. The evolutes of the variety are (iterated) envelopes of the family of its “Euclidean” normal spaces. Viewing the evolutes as singularities of a mapping, evaluation of the corresponding Thom polynomials yields numerical formulas. For curves and surfaces, the formulas agree with those of Salmon in the cases considered by him.