3-dimensional Levi-Civita metrics with projective vector fields

被引：1

作者：

Manno, Gianni ^{[1
]}

Vollmer, Andreas ^{[1
]}

机构：

[1] Politecn Torino, Dipartimento Sci Matemat, Corso Duca Abruzzi,24, I-10129 Turin, TO, Italy

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2022年 / 163卷

关键词：

Levi-Civita metrics; Projective vector fields; Projectively equivalent metrics; NORMAL FORMS;

D O I：

10.1016/j.matpur.2022.05.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Projective vector fields are the infinitesimal transformations whose local flow preserves geodesics up to reparametrisation. In 1882, Sophus Lie posed the problem of describing 2-dimensional metrics admitting a non-trivial projective vector field, which was solved in recent years. In the present paper, we solve the analog of Lie's problem in dimension 3, for Riemannian metrics and, more generally, for Levi-Civita metrics of arbitrary signature. (c) 2022 Elsevier Masson SAS. All rights reserved.

引用

页码：473 / 517

页数：45

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