A solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields

preprint2007arXivOpen access

We give a complete list of normal forms for the 2-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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A solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields

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