On Calderon's problem for the connection Laplacian

Abstract

We consider Calderon's problem for the connection Laplacian on a real-analytic vector bundle over a manifold with boundary. We prove a uniqueness result for this problem when all geometric data are real-analytic, recovering the topology and geometry of a vector bundle up to a gauge transformation and an isometry of the base manifold.

21 pages, final version; inaccuracies corrected, stylistic changes made, new references added