On the flat geometry of the cuspidal edge

zbMath1400.57028arXiv1610.08702MaRDI QIDQ1667184

Farid Tari, Raul Oset Sinha

Publication date: 27 August 2018

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

Full work available at URL: https://arxiv.org/abs/1610.08702

zbMATH Keywords

generic singularitytransversalitycuspidal edgesubmersionMather groupsingularity of a function

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Singularities of differentiable mappings in differential topology (57R45)

Related Items (18)

Behavior of principal curvatures of frontals near non-front singular points and their applications ⋮ Local theory of singularities of three functions and the product maps ⋮ Singularities of Gauss maps of wave fronts with non-degenerate singular points ⋮ Geometry of cuspidal edges with boundary ⋮ Axial curvatures for corank 1 singular \(n\)-manifolds in \(\mathbb{R}^{n+k}\) ⋮ Framed surfaces in the Euclidean space ⋮ Singularities of Gauss maps of frontal surfaces with non-front singular points ⋮ The flat geometry of the I_1 singularity: (x,y) -> (x,xy,y^2,y^3) ⋮ Focal surfaces of fronts associated to unbounded principal curvatures ⋮ The Gauss-Bonnet type theorem for future directed fronts in hyperbolic 3-space and de Sitter 3-space ⋮ On the index of principal foliations of surfaces in R^3 with corank 1 singularities ⋮ The geometry of corank 1 surfaces in ℝ4 ⋮ Geometry of bifurcation sets of generic unfoldings of corank two functions ⋮ On Gaussian curvatures and singularities of Gauss maps of cuspidal edges ⋮ Singularities of a surface given by Kenmotsu-type formula in Euclidean three-space ⋮ Dualities of differential geometric invariants on cuspidal edges on flat fronts in the hyperbolic space and the De Sitter space ⋮ Principal curvatures and parallel surfaces of wave fronts ⋮ Criteria for sharksfin and deltoid singularities from the plane into the plane and their applications

Cites Work

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• Topological triviality and versality for subgroups of 𝐴 and 𝐾
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• Projections of Piecewise-Smooth Surfaces
• Functions on a crosscap
• Computational Aspects of Classifying Singularities
• Singularities of general one-dimensional motions of the plane and space

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