A unitary connection is a vector bundle connection that preserves a Hermitian inner product.
On a trivial bundle 
, write 
, where 
is a matrix-valued differential
form of degree one satisfying 
. Under a smooth unitary change
of frame 
,
its connection form becomes
 |
For a Riemannian metric 
, the operator 
is the connection
Laplacian; the adjoint uses 
and the Hermitian inner
product. Its Dirichlet-to-Neumann
operator is invariant under unitary changes of frame
equal to the identity on the boundary. When the Riemannian
metric is also varied, a simultaneous pullback by a diffeomorphism
fixing the boundary preserves these measurements.
