A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields
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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.
Published Version (Please cite this version)10.1007/s00208-007-0158-3
Publication InfoBryant, RL; Manno, G; & Matveev, VS (2008). A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields. Mathematische Annalen, 340(2). pp. 437-463. 10.1007/s00208-007-0158-3. Retrieved from https://hdl.handle.net/10161/13154.
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Phillip Griffiths Professor of Mathematics
My research concerns problems in the geometric theory of partial differential equations. More specifically, I work on conservation laws for PDE, Finsler geometry, projective geometry, and Riemannian geometry, including calibrations and the theory of holonomy. Much of my work involves or develops techniques for studying systems of partial differential equations that arise in geometric problems. Because of their built-in invariance properties, these systems often have specia