BEHAVIOR OF CORANK-ONE SINGULAR POINTS ON WAVE FRONTS

Abstract

Let M2 be an oriented 2-manifold and f : M2→R3 a C∞-map. A point p ∈M2 is called a singular point if f is not an immersion at p. The map f is called a front (or wave front), if there exists a unit C∞-vector field ν such that the image of each tangent vector df (X) (X ∈ TM2) is perpendicular to ν, and the pair (f, ν) gives an immersion into R3 × S2. In a previous paper, we gave an intrinsic formulation of wave fronts in R3. In this paper, we investigate the behavior of cuspidal edges near corank-one singular points and establish Gauss-Bonnet-type formulas under the intrinsic formulation.