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

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Abstract

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.

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Authors and Affiliations

  1. Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, CA, 94720-5070, USA

    Robert L. Bryant

  2. Department of Mathematics, via per Arnesano, 73100, Lecce, Italy

    Gianni Manno

  3. Institute of Mathematics, FSU Jena, 07737, Jena, Germany

    Vladimir S. Matveev

Authors
  1. Robert L. Bryant
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  2. Gianni Manno
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  3. Vladimir S. Matveev
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Correspondence to Vladimir S. Matveev.

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Bryant, R.L., Manno, G. & Matveev, V.S. A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields. Math. Ann. 340, 437–463 (2008). https://doi.org/10.1007/s00208-007-0158-3

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