3D Mappings by Generalized Joukowski Transformations

  • Carla Cruz
  • M. I. Falcão
  • H. R. Malonek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6784)


The classical Joukowski transformation plays an important role in different applications of conformal mappings, in particular in the study of flows around the so-called Joukowski airfoils. In the 1980s H. Haruki and M. Barran studied generalized Joukowski transformations of higher order in the complex plane from the view point of functional equations. The aim of our contribution is to study the analogue of those generalized Joukowski transformations in Euclidean spaces of arbitrary higher dimension by methods of hypercomplex analysis. They reveal new insights in the use of generalized holomorphic functions as tools for quasi-conformal mappings. The computational experiences focus on 3D-mappings of order 2 and their properties and visualizations for different geometric configurations, but our approach is not restricted neither with respect to the dimension nor to the order.


Generalized Joukowski transformation quasi-conformal mappings hypercomplex differentiable functions 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Carla Cruz
    • 1
  • M. I. Falcão
    • 2
  • H. R. Malonek
    • 1
  1. 1.Departamento de MatemáticaUniversidade de AveiroPortugal
  2. 2.Departamento de Matemática e AplicaçõesUniversidade do MinhoPortugal

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