Singularities of parallel surfaces (Q1762346)

The authors investigate singularities of all surfaces \( g^t \) parallel to a given regular surface \( g \) in \( \mathbb R^3 \). The types of singularities of parallel surfaces are cuspidal edges, swallowtails, cuspidal lips, cuspidal beaks, cuspidal butterfly and \(3\)-dimensional \(D_4^\pm\) singularities. The main theorems (Theorems 3.4 and 3.5) give criteria for these singularity types of \( g^t\) for all \( t \) in terms of differential geometry.