Formes normales pour les champs conformes pseudo-riemanniens

2010/08/23 by Charles Frances, Frances, Charles, Karin Melnick +1 · 1 citation
Mathematics · Physics and Astronomy · #53B30 #53C27 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.DG #math.DS #msc:53B30 #msc:53C27

paper · pdf · doi:10.48550/arxiv.1008.3781

49 pages, Minor modifications according to referee's comments. To appear in Bulletin de la SMF

arxiv created 2012/09/17 · arxiv updated 2012/09/19

Abstract

We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is conformally flat. In either case, the vector field is locally conjugate to a normal form on a model space. For smooth metrics of general signature, we obtain the analogous result under the additional assumption that the differential of the flow at the fixed point is bounded.

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