Nowhere conformally homogeneous manifolds and limiting Carleman weights

Abstract

In this note we prove that a generic Riemannian manifold of dimension $\ge 3$ 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 $\ge 3$ 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 $\ge 3$ do not admit limiting Carleman weights near any point.

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References in corpus (2)

• Inverse problems for the anisotropic Maxwell equations
• Conformal Killing forms on Riemannian manifolds