Bertrand and Mannheim curves of framed curves in the3-dimensional Euclidean space

DOI10.3906/mat-1905-63zbMath1453.53007OpenAlexW3024211945WikidataQ114022806 ScholiaQ114022806MaRDI QIDQ4970856

Shun'ichi Honda, Masatomo Takahashi

Publication date: 7 October 2020

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1905-63

zbMATH Keywords

singularityMannheim curveBertrand curveframed curve

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 (13)

Forming coupled dispersionless equations of families of Bertrand curves ⋮ Spinor representation of framed Mannheim curves ⋮ A New Generalization of Some Curve Pairs ⋮ Pedal and contrapedal curves of framed immersions in the Euclidean 3-space ⋮ The differential geometry of curves in \(B^1 \times \mathbb{R}\) ⋮ New approach to timelike Bertrand curves in 3-dimensional Minkowski space ⋮ Singularities of parallels to tangent developable surfaces ⋮ Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space ⋮ Canal surfaces generated by special curves and quaternions ⋮ Generalized osculating‐type ruled surfaces of singular curves ⋮ Unnamed Item ⋮ Normal and tangent maps to frontals ⋮ Framed curves in three-dimensional Lie groups and a Berry phase model

Cites Work

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• Evolutes and focal surfaces of framed immersions in the Euclidean space
• A variational characterization and geometric integration for Bertrand curves

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