The behavior of curvature functions at cusps and inflection points

DOI10.1016/j.difgeo.2012.04.001zbMath1250.53005arXiv1102.4478OpenAlexW2018540236WikidataQ115356723 ScholiaQ115356723MaRDI QIDQ428924

Masaaki Umehara, Shohei Shiba

Publication date: 25 June 2012

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

Full work available at URL: https://arxiv.org/abs/1102.4478

zbMATH Keywords

cuspaffine curvatureinflection point, curves with prescribed curvature

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Affine differential geometry (53A15) Differential invariants (local theory), geometric objects (53A55)

Related Items (12)

Kosambi–Cartan–Chern Analysis of the Nonequilibrium Singular Point in One-Dimensional Elementary Catastrophe ⋮ Caustics of convex curves ⋮ Koenderink type theorems for fronts ⋮ Geometry of cuspidal edges with boundary ⋮ Duality on generalized cuspidal edges preserving singular set images and first fundamental forms ⋮ Local differential geometry of cuspidal edge and swallowtail ⋮ On Gaussian curvatures and singularities of Gauss maps of cuspidal edges ⋮ Inflection points on 3D curves ⋮ Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts ⋮ Singularities of singular solutions of first-order differential equations of clairaut type ⋮ Principal curvatures and parallel surfaces of wave fronts ⋮ Capturing information on curves and surfaces from their projected images

Cites Work

• Unnamed Item
• A simplification of the proof of Bol's conjecture on sextactic points
• The duality between singular points and inflection points on wave fronts
• Affine-invariant distances, envelopes and symmetry sets
• On a conjecture of G. Bol.
• Generic affine differential geometry of plane curves

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