On Lie’s functional equation of translation type
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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
Keywords.Functional equation of translation type translation surfaces paraboloids surfaces in Galois spaces
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