Formes normales pour les champs conformes pseudo-riemanniens

Charles Frances; Karin Melnick

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arXiv · 1008.3781

Formes normales pour les champs conformes pseudo-riemanniens

Charles Frances·Karin Melnick

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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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Charles Frances, Karin Melnick. 2012-09-17. Formes normales pour les champs conformes pseudo-riemanniens. https://arxiv.org/abs/1008.3781

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