Oriented and nonoriented curvature varifolds

In a recent work, G. Anzellotti and the present authors introduced a notion of variation for functions defined over a rectifiable current. In this paper, we give a definition of a curvature varifold slightly different from that of Hutchinson (equivalent in the nonoriented case) and we study the variation properties, in the sense of [2], of the normal to a rectifiable current when the associated varifold is a curvature varifold.