A curved structure consisting of an imperfectly conducting circular cylinder coated by any number of coaxial thin anisotropic layers separated by isotroplc regions of different materials is considered. Each thin anisotroplc layer is represented by a sheet with an anisotropic Jump Impedance. Thus, the structure is a generalization to the anisotropic case of Jaumann absorbers on curved surfaces. For a normally incident and obliquely polarized plane wave, the scattered field is determined via a chain-matrix algorithm. An optimization procedure is developed to minimize the radar cross section over an assigned frequency band by varying the geometric and electromagnetic parameters of the structure. Numerical results based on this design procedure are presented and discussed.