Local differential geometry of cuspidal edge and swallowtail

zbMath1461.53002MaRDI QIDQ2215995

Toshizumi Fukui

Publication date: 15 December 2020

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1602230468

zbMATH Keywords

invariantedgeswallowtail

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Critical points of functions and mappings on manifolds (58K05)

Related Items (8)

Approximating singularities by a cuspidal-edge on a maxface ⋮ Normal form of the swallowtail and its applications ⋮ Singularities of Gauss maps of frontal surfaces with non-front singular points ⋮ Framed surfaces and one-parameter families of framed curves in Euclidean 3-space ⋮ Focal surfaces of fronts associated to unbounded principal curvatures ⋮ On Gaussian curvatures and singularities of Gauss maps of cuspidal edges ⋮ Dualities of differential geometric invariants on cuspidal edges on flat fronts in the hyperbolic space and the De Sitter space ⋮ Criteria for sharksfin and deltoid singularities from the plane into the plane and their applications

Cites Work

• The behavior of curvature functions at cusps and inflection points
• Flat surfaces with singularities in Euclidean 3-space
• Singularities of maximal surfaces
• Singularities of parallel surfaces
• The geometry of fronts
• Singularities of flat fronts in hyperbolic space
• Geometric Invariants of Cuspidal Edges
• Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts
• On the Classification of Germs of Maps from R² to R³
• Normal form of the swallowtail and its applications
• Cuspidal edges with the same first fundamental forms along a knot
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