Framed surfaces in the Euclidean space

DOI10.1007/s00574-018-0090-zzbMath1425.58021OpenAlexW2706552694MaRDI QIDQ2422781

Tomonori Fukunaga, Masatomo Takahashi

Publication date: 20 June 2019

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://muroran-it.repo.nii.ac.jp/?action=repository_action_common_download&item_id=10182&item_no=1&attribute_id=24&file_no=1

zbMATH Keywords

curvaturesingular pointfrontalbasic invariantframed surface

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Surfaces in Euclidean and related spaces (53A05) Singularities of differentiable mappings in differential topology (57R45) Critical points of functions and mappings on manifolds (58K05)

Related Items (15)

Behavior of principal curvatures of frontals near non-front singular points and their applications ⋮ Surfaces of revolution of frontals in the Euclidean space ⋮ The fundamental theorem for singular surfaces with limiting tangent planes ⋮ One‐parameter families of Legendre curves and plane line congruences ⋮ Framed surfaces and one-parameter families of framed curves in Euclidean 3-space ⋮ Extendibility and boundedness of invariants on singularities of wavefronts ⋮ Tubular surfaces associated with framed base curves in Euclidean 3‐space ⋮ Focal surfaces of fronts associated to unbounded principal curvatures ⋮ Caustics of pseudo-spherical surfaces in the Euclidean 3-space ⋮ Generalized osculating‐type ruled surfaces of singular curves ⋮ On the evolution of framed curves in Euclidean 3‐space ⋮ Envelopes of families of framed surfaces and singular solutions of first-order partial differential equations ⋮ On Gaussian curvatures and singularities of Gauss maps of cuspidal edges ⋮ Envelopes of one-parameter families of framed curves in the Euclidean space ⋮ Singularities of translation surfaces in the Euclidean 3-space

Uses Software

• CandS

Cites Work

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• Fronts of Whitney umbrella – a differential geometric approach via blowing up

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