A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields
TLDR
In this article, a complete list of normal forms for the two-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations is given, and it is shown that these normal forms are mutually non-isometric.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.read more
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Proof of the Projective Lichnerowicz Conjecture for Pseudo-Riemannian Metrics with Degree of Mobility Greater than Two
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References
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TL;DR: In this paper, the authors present a Lie Group Analysis of Ordinary Differential Equations (ODE) for the first order and second order differential equations, respectively, and integrate them into Third Order Equations.
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Sur les variétés à connexion projective
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