aequationes mathematicae

, Volume 68, Issue 3, pp 127–159 | Cite as

On Lie’s functional equation of translation type

Research paper


The functional equation of translation type, as originally introduced by Sophus Lie, will be solved for the paraboloid under various regularity assumptions and in different algebraic situations. Real paraboloids are characterized as surfaces permitting two special decompositions as sum of two curves. Moreover, we show that such a characterization does not generally hold true for paraboloids in Galois spaces. Finally, some problems related to a generalization of Lie’s functional equation are presented.

Mathematics Subject Classification (2000).

39B12 39B22 39B52 14J25 51E25 53A05 


Functional equation of translation type translation surfaces paraboloids surfaces in Galois spaces 


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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HamburgHamburgGermany
  2. 2.Institut für MathematikKarl-Franzens-Universität GrazGrazAustria

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