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

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

2007-05-24

arxiv.org/abs/0705.3592v2

Math. Ann. 340(2008), no. 2, 437-463

Mathematics

Differential Geometry

This is an extended version of the paper that will appear in Math. Annalen. Some typos were corrected, references were updated

Scientific paper

10.1007/s00208-007-0158-3

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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