Surfaces of Osculating Circles in Euclidean Space

The aim of this paper is to define a new class of surfaces in Euclidean space using the concept of osculating circle. Given a regular curve C , the surface of osculating circles generated by C is the set of all osculating circles at all points of C . It is proved that these surfaces contain a one-parametric family of planar lines of curvature. A classification of surfaces of osculating circles is given in the family of canal surfaces, Weingarten surfaces, surfaces with constant Gauss curvature and surfaces with constant mean curvature.