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

Gianni Manno; Robert L. Bryant; Vladimir S. Matveev

arxiv: 0705.3592 · v2 · pith:SRDJ7SKInew · submitted 2007-05-24 · 🧮 math.DG · math.AP

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

Robert L. Bryant , Gianni Manno , Vladimir S. Matveev This is my paper

classification 🧮 math.DG math.AP

keywords formsnormalmetricsproblemsophusadmitadmittingcomplete

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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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