The locally enhanced sampling (LES) methodology is used for simulating molecules consisting of a small subsystem that is of interest and a larger subsystem that interacts with the smaller one. The small subsystem is replicated to enhance its sampling and the large subsystem sees the mean field of the replicated components while the replicas are energetically transparent to one another. In this work we investigate the properties of the LES potential surface. It is shown that every local energy minimum on the potential surface of the real system is also a local energy minimum on the LES potential surface. It is also demonstrated that the converse of this is not true; i.e., there are minima on the LES potential energy surface that do not correspond to any minimum on the potential surface of the real system. A quantitative measure is derived to estimate how far minima on the LES potential surface are from minima on the potential surface of the real system. The implications and potential applications of this work are discussed.