Normal forms for conformal vector fields

被引：10

作者：

Frances, Charles ^{[1
]}

Melnick, Karin ^{[2
]}

机构：

[1] Univ Paris 11, Dept Math, F-91405 Orsay, France

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

来源：

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE | 2013年 / 141卷 / 03期

基金：

美国国家科学基金会;

关键词：

D O I：

10.24033/bsmf.2652

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：377 / 421

页数：45

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