  We consider the inverse problem to determine a smooth compact Riemannian
manifold with boundary $(M, g)$ from a restriction $\Lambda_{\Src, \Rec}$ of
the Dirichlet-to-Neumann operator for the wave equation on the manifold. Here
$\Src$ and $\Rec$ are open sets in $\p M$ and the restriction $\Lambda_{\Src,
\Rec}$ corresponds to the case where the Dirichlet data is supported on
$\R_+\times \Src$ and the Neumann data is measured on $\R_+\times \Rec$. In the
novel case where $\bar \Src \cap \bar \Rec = \emptyset$, we show that
$\Lambda_{\Src, \Rec}$ determines the manifold $(M,g)$ uniquely, assuming that
the wave equation is exactly controllable from the set of sources $\Src$.
Moreover, we show that the exact controllability can be replaced by the
Hassell-Tao condition for eigenvalues and eigenfunctions, that is, \lambda_j
\le C \norm{\p_\nu \phi_j}_{L^2(\Src)}^2, \quad j =1, 2, ..., where $\lambda_j$
are the Dirichlet eigenvalues and $(\phi_j)_{j=1}^\infty$ is an orthonormal
basis of the corresponding eigenfunctions.
