A turbine engine part or set of parts including at least first and second obstacles each having a leading edge and a trailing edge, and a platform from which the obstacles extend; wherein the platform has, between the pressure side of the first obstacle and the suction side of the second obstacle a non-axisymmetric surface defining at least one fin with a substantially triangular cross-section, each fin being associated with a leading position and a trailing position on the surface between which the fin extends, such that the leading position is upstream of each of the leading edges; the trailing position is downstream of each of the leading edges.