2009/11/27 by Yuri Bozhkov, Bozhkov, Yuri, Igor Leite Freire +1
Mathematics · Physics and Astronomy · #35J20 #35J50 #35J60 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Waves and Solitons #math.AP #math.MG #msc:35J20 #msc:35J50 #msc:35J60
paper · pdf · doi:10.48550/arxiv.0911.5292
Paper submitted for publication
arxiv created 2009/11/27 · openalex publication_date 2009/11/27 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.