On Gaussian curvatures and singularities of Gauss maps of cuspidal edges

Abstract

We show relation between sign of Gaussian curvature of cuspidal edge and geometric invariants through types of singularities of Gauss map. Moreover, we define and characterize positivity/negativity of cusps of Gauss maps by geometric invariants of cuspidal edges, and show relation between sign of cusps and of the Gaussian curvature.