A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields
By Robert L. Bryant, G. Manno, V. Matveev. 2007
74 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2f11bccd7dc43bbf29fa3ea19982ceb66e1948c2
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In Astronomy and Astrophysics
In Statistical and Nonlinear Physics
Citations in the corpus
- An Invitation to Web Geometry (2011, unknown): “If L1 =2Cxy −Bxx − 3Dyy − 6DAx − 3ADx + 3DBy + 3DBy + CBx − 2CCy and L2 =2 Bxy − Cyy − 3Axx + 6ADy + 3DAy − 3ACx − 3CAy −BCy + 2BBx then, according to [22], Liouville has shown that the tensor L = ( L1dx+ L2dy ) ⊗ (dx ∧ dy) is invariant under point transformations and that the differential equation ”
- Point classification of 2nd order ODEs:Tresse classification revisited and beyond (2008, background): “This is almost obvious for projective connections (cubic ), but for metric projective connections this is already substantial, see [ BMM ].”