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Geometric Invariants of Cuspidal Edges

  Published:2016-02-11
 Printed: Apr 2016
  • Luciana de Fátima Martins,
    Departamento de Matemática, IBILCE-UNESP-Univ Estadual Paulista, R. Cristóvão Colombo, 2265, CEP 15054-000, São José do Rio Preto, SP, Brazil
  • Kentaro Saji,
    Department of Mathematics, Graduate School of Science, Kobe University, Rokko, Nada, Kobe 657-8501, Japan
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Abstract

We give a normal form of the cuspidal edge which uses only diffeomorphisms on the source and isometries on the target. Using this normal form, we study differential geometric invariants of cuspidal edges which determine them up to order three. We also clarify relations between these invariants.
Keywords: cuspidal edge, curvature, wave fronts cuspidal edge, curvature, wave fronts
MSC Classifications: 57R45, 53A05, 53A55 show english descriptions Singularities of differentiable mappings
Surfaces in Euclidean space
Differential invariants (local theory), geometric objects
57R45 - Singularities of differentiable mappings
53A05 - Surfaces in Euclidean space
53A55 - Differential invariants (local theory), geometric objects
 

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