Cuspidal edges on focal surfaces of regular surfaces with parabolic points

2025/08/31 by Teramoto, Keisuke
#53A05 #53A55 #57R45 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.00860

Abstract

We investigate geometric invariants of cuspidal edges on focal surfaces of regular surface. In particular, we shall clarify the sign of the singular curvature at a cuspidal edge on a focal surface using singularities of parallel surface of a given surface satisfying certain conditions.

Citations

• Focal surfaces of fronts associated to unbounded principal curvatures
• Extendibility and boundedness of invariants on singularities of wavefronts
• On the flat geometry of the cuspidal edge
• Geometric invariants of cuspidal edges
• Behavior of Gaussian curvature and mean curvature near non-degenerate singular points on wave fronts
• Singularities of parallel surfaces
• The geometry of fronts

Related

• The geometry of fronts
• Isometric deformations of cuspidal edges
• Geometric invariants of 5/2-cuspidal edges
• Geometric invariants of cuspidal edges
• On the flat geometry of the cuspidal edge