A₂-singularities of hypersurfaces with non-negative sectional curvature in Euclidean space

Abstract

In a previous work, the authors gave a definition of `front bundles'. Using this, we give a realization theorem for wave fronts in space forms, like as in the fundamental theorem of surface theory. As an application, we investigate the behavior of principal singular curvatures along A₂-singularities of hypersurfaces with non-negative sectional curvature in Euclidean space.