Nowhere conformally homogeneous manifolds and limiting Carleman weights

Details Nowhere conformally homogeneous manifolds and limiting Carleman weights Nowhere conformally homogeneous manifolds and limiting Carleman weights

2010-11-10

arxiv.org/abs/1011.2507v1

Mathematics

Differential Geometry

8 pages, no figures

Scientific paper

In this note we prove that a generic Riemannian manifold of dimension $\geq 3$ 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 $\geq 3$ do not admit nontrivial conformal Killing vector fields near any point. As an application to the inverse problem of Calder\'on on manifolds, this implies that generic manifolds of dimension $\geq 3$ do not admit limiting Carleman weights near any point.

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