Envelopes of families of framed surfaces and singular solutions of first-order partial differential equations

DOI10.1017/prm.2020.71zbMath1478.58013OpenAlexW3199073613WikidataQ115337083 ScholiaQ115337083MaRDI QIDQ5152534

Haiou Yu, Masatomo Takahashi

Publication date: 24 September 2021

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/prm.2020.71

zbMATH Keywords

singular solutionspartial differential equationsfoliationsenvelopescompletely integrable equationsfamily of framed surfaces

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Singularities of differentiable mappings in differential topology (57R45) Initial value problems for nonlinear first-order PDEs (35F25) Differential invariants (local theory), geometric objects (53A55) Critical points of functions and mappings on manifolds (58K05) Initial value problems for systems of nonlinear first-order PDEs (35F55)

Uses Software

• CandS

Cites Work

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• Sur la théorie des enveloppes
• Envelopes of families of Legendre mappings in the unit tangent bundle over the Euclidean space
• A characterization of complete integrability for partial differential equations of first order
• Framed surfaces in the Euclidean space
• Geometric Invariants of Cuspidal Edges
• Differential Geometry from a Singularity Theory Viewpoint
• LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
• Singular Solutions of First-Order Differential Equations