A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields
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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Journal articlePermalink
https://hdl.handle.net/10161/13154Published Version (Please cite this version)
10.1007/s00208-007-0158-3Publication Info
(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.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Robert Bryant
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
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