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    Surfaces of Osculating Circles in Euclidean Space
    (Springer Singapore Pte Ltd, 2024) Lopez, Rafael; Camcı, Çetin; Uçum, Ali; İlarslan, Kazım
    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.