  We reconstruct a Riemannian manifold and a Hermitian vector bundle with
compatible connection from the hyperbolic Dirichlet-to-Neumann operator
associated with the wave equation of the connection Laplacian. The boundary
data is local and the reconstruction is up to the natural gauge transformations
of the problem. As a corollary we derive an elliptic analogue of the main
result which solves a Calderon problem for connections on a cylinder.
