Special Conformal Groups of a Riemannian Manifold and Lie Point Symmetries of the Nonlinear Poisson Equation

Autor:	Bozhkov, Yuri, Freire, Igor Leite
Rok vydání:	2009
Předmět:	Mathematics - Analysis of PDEs Mathematics - Metric Geometry 35J50 35J20 35J60
Druh dokumentu:	Working Paper
Popis:	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. Comment: Paper submitted for publication
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0911.5292 Zobrazit plný text záznamu View this record from Arxiv