Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson equation

被引：40

作者：

Bozhkov, Yuri ^{[1
]}

Freire, Igor Leite ^{[1
,2
]}

机构：

[1] Univ Estadual Campinas, IMECC, BR-13083970 Campinas, SP, Brazil

[2] Univ Fed ABC UFABC, Ctr Matemat Comp & Cognicao, BR-09090400 Santo Andre, SP, Brazil

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 249卷 / 04期

基金：

巴西圣保罗研究基金会;

关键词：

Lie point symmetry; Noether symmetry; Conservation laws; Conformal group; PARTIAL-DIFFERENTIAL-EQUATIONS; DIRECT CONSTRUCTION METHOD; CONSERVATION-LAWS; GROUP CLASSIFICATION; WAVE-EQUATION; SURFACES;

D O I：

10.1016/j.jde.2010.04.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on M are special subgroups of the conformal group of M. In particular, if the scalar curvature of M vanishes, the projection on M of the Lie point symmetry group of the Poisson equation with critical nonlinearity is the conformal group of the manifold. We illustrate our results by applying them to the Thurston geometries. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：872 / 913

页数：42