  In this paper, we give some simple counterexamples to uniqueness for the
Calderon problem on Riemannian manifolds with boundary when the Dirichlet and
Neumann data are measured on disjoint sets of the boundary. We provide
counterexamples in the case of two and three dimensional Riemannian manifolds
with boundary having the topology of circular cylinders in dimension two and
toric cylinders in dimension three. The construction could be easily extended
to higher dimensional Riemannian manifolds.
