The Gauss map of a hypersurface in Euclidean sphere and the spherical Legendrian duality

DOI10.1016/J.TOPOL.2011.09.030zbMath1235.53013OpenAlexW2004908752MaRDI QIDQ664673

Takayuki Nagai

Publication date: 2 March 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2011.09.030

zbMATH Keywords

singularitieshypersurfacesGauss mapsEuclidean spherewavefront setbifurcation setscontact between hypersurfacesfamily of height functionsspherical Legendrian duality

Mathematics Subject Classification ID

Singularities of differentiable mappings in differential topology (57R45) Non-Euclidean differential geometry (53A35)

Related Items (7)

Lightcone dualities for hypersurfaces in the sphere ⋮ Evolutes of spacelike hypersurfaces in anti-de Sitter space ⋮ Singularities of helix surfaces in Euclidean 3-space ⋮ Gauss maps and duality of sphere bundles ⋮ Legendre curves in the unit spherical bundle over the unit sphere and evolutes ⋮ Lightcone dualities for curves in the lightcone unit 3-sphere ⋮ Great circular surfaces in the three-sphere

Cites Work

• Unnamed Item
• Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol'd
• Reconstructions of fronts and caustics depending on a parameter and versality of mappings
• On contact between submanifolds
• Stability of caustics
• Lagrangian and Legendrian singularities
• SINGULARITIES OF EVOLUTES OF HYPERSURFACES IN HYPERBOLIC SPACE

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