Contact properties of surfaces in \({\mathbb R}^3\) with corank 1 singularities

DOI10.2748/tmj/1429549581zbMath1320.58023OpenAlexW2172116310MaRDI QIDQ2346202

Luciana F. Martins, Juan Jose Nuño-Ballesteros

Publication date: 29 May 2015

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.tmj/1429549581

zbMATH Keywords

singular surfacesWhitney umbrellaumbilic curvaturecurvature parabolacross-cap

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Singularities of differentiable mappings in differential topology (57R45) Critical points of functions and mappings on manifolds (58K05)

Related Items (17)

Isometric deformations of cuspidal edges ⋮ Singularities of Gauss maps of wave fronts with non-degenerate singular points ⋮ On the flat geometry of the cuspidal edge ⋮ 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 ⋮ The flat geometry of the I_1 singularity: (x,y) -> (x,xy,y^2,y^3) ⋮ On the index of principal foliations of surfaces in R^3 with corank 1 singularities ⋮ The geometry of corank 1 surfaces in ℝ4 ⋮ Relating second order geometry of manifolds through projections and normal sections ⋮ Geometry of surfaces in \(\mathbb{R}^5\) through projections and normal sections ⋮ On the geometry of folded cuspidal edges ⋮ Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts ⋮ Singular 3-manifolds in \(\mathbb{R}^5\) ⋮ A relation between the curvature ellipse and the curvature parabola ⋮ The axial curvature for corank 1 singular surfaces ⋮ Principal curvatures and parallel surfaces of wave fronts

Cites Work

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• Lines of principal curvature around umbilics and Whitney umbrellas
• The geometry of surfaces in 4-space from a contact viewpoint
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• The geometry of fronts
• On pairs of geometric foliations on a cross-cap
• Isolated roundings and flattenings of submanifolds in Euclidean spaces
• Intrinsic invariants of cross caps
• Geometric Invariants of Cuspidal Edges
• On the Classification of Germs of Maps from R² to R³
• Generic Curves and Surfaces
• Functions on a crosscap
• Fronts of Whitney umbrella – a differential geometric approach via blowing up
• Height functions on Whitney umbrellas
• Surfaces in $\mathbb{R}^4$ and their projections to 3-spaces

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