Projections of surfaces in \(\mathbb R^4\) to \(\mathbb R^3\) and the geometry of their singular images

DOI10.4171/RMI/825zbMath1316.57021OpenAlexW2233329412MaRDI QIDQ2340459

Raul Oset Sinha, Farid Tari

Publication date: 17 April 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rmi/825

zbMATH Keywords

projections\(\mathcal{A}\)-singularitysingular surfaces in \(\mathbb{R}^3\)surfaces in \(\mathbb{R}^4\)

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Singularities of differentiable mappings in differential topology (57R45) Affine differential geometry (53A15)

Related Items (16)

Isometric deformations of cuspidal edges ⋮ On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations ⋮ Normal form of the swallowtail and its applications ⋮ Curvature loci of 3‐manifolds ⋮ 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 ⋮ Cross-ratio invariants for surfaces in 4-space ⋮ A relation between the curvature ellipse and the curvature parabola ⋮ The axial curvature for corank 1 singular surfaces ⋮ Contact properties of surfaces in \({\mathbb R}^3\) with corank 1 singularities

Cites Work

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• On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations
• Lines of principal curvature around umbilics and Whitney umbrellas
• On singularities of submanifolds of higher dimensional Euclidean spaces
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• Lines of curvature on surfaces immersed in ?4
• Functions on a crosscap
• FAMILIES OF SURFACES IN ℝ⁴
• Inflection points and topology of surfaces in 4-space
• Fronts of Whitney umbrella – a differential geometric approach via blowing up

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