The theory of graph-like Legendrian unfoldings and its applications

DOI10.5427/jsing.2015.12dzbMath1314.58022arXiv1410.8678OpenAlexW2963885124MaRDI QIDQ5174929

Shyuichi Izumiya

Publication date: 19 February 2015

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

Full work available at URL: https://arxiv.org/abs/1410.8678

zbMATH Keywords

Lagrangian singularitiescausticsbig wave frontswave front propagationsgraph-like Legendrian unfoldings

Mathematics Subject Classification ID

Singularities of differentiable mappings in differential topology (57R45) Local complex singularities (32S05) Critical points of functions and mappings on manifolds (58K05) Deformation of singularities (58K60) Stability theory for manifolds (58K25)

Related Items (2)

Caustics of world hyper-sheets in the Minkowski space-time ⋮ On families of Lagrangian submanifolds

Cites Work

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• Lightlike hypersurfaces along spacelike submanifolds in Minkowski space-time
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• Lagrangian and Legendrian singularities
• Reconstructions of wave fronts depending on one parameter
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• Geometric singularities for solutions of single conservation laws
• Holonomic systems of Clairaut type
• Spacelike parallels and evolutes in Minkowski pseudo-spheres
• The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space
• Singularities of caustics in generic translation-invariant control problems
• The normal singularities of a submanifold
• Lightlike hypersurfaces along spacelike submanifolds in de Sitter space
• Geometry of world sheets in Lorentz-Minkowski space
• Caustics of world hyper-sheets in the Minkowski space-time
• The holographic principle
• The unfolding and determinacy theorems for subgroups of 𝒜 and 𝒦
• CLASSIFICATION OF GENERIC INTEGRAL DIAGRAMS AND FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
• Wavefronts and parallels in Euclidean space
• Completely integrable holonomic systems of first-order differential equations
• Pedal foliations and Gauss maps of hypersurfaces in Euclidean space

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