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. © 2007 Springer-Verlag.
Bryant, R., Manno, G., Matveev, V. (2008). A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields. MATHEMATISCHE ANNALEN, 340(2), 437-463 [10.1007/s00208-007-0158-3].
A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields
MANNO, GIOVANNI;
2008
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. © 2007 Springer-Verlag.
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