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

Abstract

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.

This is an extended version of the paper that will appear in Math. Annalen. Some typos were corrected, references were updated, title was changed (as in the journal version). 31 pages

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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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