Involutes of fronts in the Euclidean plane

DOI10.1007/s13366-015-0275-1zbMath1352.58007OpenAlexW2281799305MaRDI QIDQ304551

Masatomo Takahashi, Tomonori Fukunaga

Publication date: 25 August 2016

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10258/00009010

zbMATH Keywords

curvatureinflection pointswave frontsreal plane curvesevolutesevolventsinvolutesLegendre immersion

Mathematics Subject Classification ID

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

Related Items (11)

A characterization of involutes and evolutes of a given curve in $\mathbb{E}^{n}$ ⋮ Some geometric characterizations of \(f\)-curves associated with a plane curve via vector fields ⋮ On involutes of order k of a null Cartan curve in Minkowski spaces ⋮ One‐parameter families of Legendre curves and plane line congruences ⋮ On (contra)pedals and (anti)orthotomics of frontals in de Sitter 2‐space ⋮ Ruled surfaces and tangent bundle of unit 2-sphere ⋮ Unnamed Item ⋮ Evolutes and involutes of frontals in the Euclidean plane ⋮ On Legendre curves in normed planes ⋮ Enveloids of Legendre curves in the unit tangent bundle over the Euclidean plane ⋮ Equi-affine plane curves with singular points

Uses Software

• CandS

Cites Work

• Existence and uniqueness for Legendre curves
• Curves in the Minkowski plane and their contact with pseudo-circles
• Reconstructions of fronts and caustics depending on a parameter and versality of mappings
• Singularities of families of evolvents in the neighborhood of an inflection point of the curve, and the group \(H_ 3\) generated by reflections
• Evolutes of hyperbolic plane curves
• Evolutes and involutes of frontals in the Euclidean plane
• Involutes of polygons of constant width in Minkowski planes
• Evolutes and Involutes of Spatial Curves
• Evolutes of fronts in the Euclidean plane
• CRITICAL POINTS OF FUNCTIONS ON A MANIFOLD WITH BOUNDARY, THE SIMPLE LIE GROUPSB_k,C_k, ANDF₄AND SINGULARITIES OF EVOLUTES
• Simple Singularities of Mappings C, 0 → C² , 0
• Symplectic Bifurcations of Plane Curves and Isotropic Liftings
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