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Contributions to the theory of Lie’s functional equation of translation type

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Abstract

The functional equation of translation surfaces as introduced by Sophus Lie will be solved under various assumptions stemming from analysis, algebra or geometry. Quadratic functions are, especially, of interest in this connection. Some general solutions will be presented. The functional equation of twofold translation surfaces will be studied in different situations. For further results in the context of Lie’s functional equation of translation type see our paper (Benz and Reich, in Aequat Math 68:127–159, 2004).

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Authors and Affiliations

  1. Hirschbergerstraße 37, 23879, Mölln, Germany

    Walter Benz

  2. Institut für Mathematik, Karl-Franzens-Universität Graz, Heinrichstr. 36/4, 8010, Graz, Austria

    Ludwig Reich

Authors
  1. Walter Benz
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  2. Ludwig Reich
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Correspondence to Ludwig Reich.

Additional information

The authors would like to thank the Austrian Academy of Sciences (Wien), the Wilhelm Blaschke Foundation (Hamburg) and also the Austrian Mathematical Society (Wien) for financial support of this project.

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Benz, W., Reich, L. Contributions to the theory of Lie’s functional equation of translation type. J. Geom. 95, 1–30 (2009). https://doi.org/10.1007/s00022-009-0014-6

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  • DOI: https://doi.org/10.1007/s00022-009-0014-6

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