2010/11/10 by Tony Liimatainen, Mikko Salo · 1 citation
Mathematics · #math.DG #math.AP #msc:53A30 #msc:35R30
published as Inverse Problems and Imaging 6, Issue 3, (2012), 523-530 · 8 pages, no figures
arxiv created 2010/11/10 · arxiv updated 2012/09/11
In this note we prove that a generic Riemannian manifold of dimension ≥ 3 does not admit any nontrivial local conformal diffeomorphisms. This is a conformal analog of a result of Sunada concerning local isometries, and makes precise the principle that generic manifolds in high dimensions do not have conformal symmetries. Consequently, generic manifolds of dimension ≥ 3 do not admit nontrivial conformal Killing vector fields near any point. As an application to the inverse problem of Calderón on manifolds, this implies that generic manifolds of dimension ≥ 3 do not admit limiting Carleman weights near any point.