Great circular surfaces in the three-sphere

DOI10.1016/j.difgeo.2011.02.005zbMath1218.53054OpenAlexW2132958298WikidataQ115356970 ScholiaQ115356970MaRDI QIDQ546129

Kentaro Saji, Shyuichi Izumiya, Takayuki Nagai

Publication date: 24 June 2011

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

Full work available at URL: http://hdl.handle.net/2115/46790

zbMATH Keywords

singularities3-spherespherical geometryextrinsic flat surfacegreat circlegreat circular surface

Mathematics Subject Classification ID

Global submanifolds (53C40) Singularities of differentiable mappings in differential topology (57R45) Classification; finite determinacy of map germs (58K40)

Related Items (11)

Legendrian dual surfaces of a spacelike curve in the 3-dimensional lightcone ⋮ Singularities of tangent surfaces to generic space curves ⋮ Circular surfaces with split quaternionic representations in Minkowski 3-space ⋮ Isometric immersions with singularities between space forms of the same positive curvature ⋮ Duality of singularities for flat surfaces in Euclidean space ⋮ Singularity properties of timelike circular surfaces in Minkowski 3-space ⋮ Gauss maps and duality of sphere bundles ⋮ Extrinsic flat surfaces along a curve on a surface in the unit three-sphere ⋮ Anti de Sitter horospherical flat timelike surfaces ⋮ The construction of circular surfaces with quaternions ⋮ Characterization of manifolds of constant curvature by ruled surfaces

Cites Work

• Unnamed Item
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• 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
• The Gauss map of a hypersurface in Euclidean sphere and the spherical Legendrian duality
• Flat surfaces with singularities in Euclidean 3-space
• Singularities of maximal surfaces
• The duality between singular points and inflection points on wave fronts
• Singularities of flat fronts in hyperbolic space
• The general type of singularity of a set of \(2n-1\) smooth functions of \(n\) variables
• Singularities of ruled surfaces in ℝ³
• Sphere stratifications and the Gauss map
• SINGULARITIES OF THE TANGENT DEVELOPABLE SURFACE OF A SPACE CURVE
• The form of the tangent-developable at points of zero torsion on space curves
• DEVELOPABLE OF A CURVE AND DETERMINACY RELATIVE TO OSCULATION-TYPE
• The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and "flat" spacelike surfaces
• Circular surfaces
• Horospherical flat surfaces in hyperbolic 3-space

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