Boundary determination of the Riemannian metric from Cauchy data for the Stokes equations

For a compact connected Riemannian manifold of dimension $n$ with smooth boundary, $n⩾2$, we prove that the Cauchy data (or the Dirichlet-to-Neumann map) for the Stokes equations uniquely determines the partial derivatives of all orders of the metric on the boundary of the manifold.