Equi-affine plane curves with singular points

DOI10.1007/s00022-022-00632-8zbMath1494.53013OpenAlexW4213445462MaRDI QIDQ2116827

Masatomo Takahashi

Publication date: 18 March 2022

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-022-00632-8

zbMATH Keywords

equi-affine evoluteequi-affine framed curveequi-affine involuteequi-affine plane curve

Mathematics Subject Classification ID

Singularities of differentiable mappings in differential topology (57R45) Curves in Euclidean and related spaces (53A04) Affine differential geometry (53A15) Critical points of functions and mappings on manifolds (58K05)

Cites Work

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• Involutes of fronts in the Euclidean plane
• Existence and uniqueness for Legendre curves
• A simplification of the proof of Bol's conjecture on sextactic points
• Affine-invariant distances, envelopes and symmetry sets
• Framed curves in the Euclidean space
• Singular points of the Wigner caustic and affine equidistants of planar curves
• Geometric invariants of \(5/2\)-cuspidal edges
• Existence conditions of framed curves for smooth curves
• Evolutes and involutes of frontals in the Euclidean plane
• Evolutes of fronts in the Euclidean plane
• Differential Geometry from a Singularity Theory Viewpoint
• Simple Singularities of Mappings C, 0 → C² , 0
• Generic affine differential geometry of plane curves
• Sextactic points on a simple closed curve

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