Mathematische Annalen

, Volume 340, Issue 2, pp 437–463 | Cite as

A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields

  • Robert L. Bryant
  • Gianni Manno
  • Vladimir S. Matveev


We give a complete list of normal forms for the two-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie.


Normal Form Constant Curvature Connected Domain Regular Point Projective Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Robert L. Bryant
    • 1
  • Gianni Manno
    • 2
  • Vladimir S. Matveev
    • 3
  1. 1.Mathematical Sciences Research InstituteBerkeleyUSA
  2. 2.Department of MathematicsLecceItaly
  3. 3.Institute of MathematicsFSU JenaJenaGermany

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