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

2010/11/06 by Saji, Kentaro, Umehara, Masaaki, Yamada, Kotaro
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 57R45 #Secondary 53A05

paper · doi:10.48550/arxiv.1011.1544

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.

Related

• The fundamental theorem for singular surfaces with limiting tangent planes
• Focal surfaces of fronts associated to unbounded principal curvatures
• Extendibility and boundedness of invariants on singularities of wavefronts
• Criteria for D₄ singularities of wave fronts
• Singular Minimal Hypersurfaces and Scalar Curvature