General relation between surface impedance and surface curvature

We relate in a general way the surface impedance of a metal to the local curvature of the surface. We obtain the corrections to the flat-surface impedance formula up to second order in dΔ, where d is the penetration depth of the electromagnetic field and Δ is the difference between maximum and minimum curvature. We give explicit expressions relating to each other the electric and magnetic fields parallel to the surface, E|| and H||, respectively. We show that the terms neglected in the surface impedance approximation contain only the second derivatives of these fields in the plane tangent to the surface.