Lopez, RafaelCamcı, ÇetinUçum, Aliİlarslan, Kazım2024-02-202024-02-202024López, R., Camci, Ç., Uçum, A., & İlarslan, K. (2024). Surfaces of Osculating Circles in Euclidean Space. Vietnam Journal of Mathematics, 52(1), 197–210. https://doi.org/10.1007/s10013-022-00585-02305-221X2305-2228https://doi.org/10.1007/s10013-022-00585-0https://hdl.handle.net/20.500.12428/5689The 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.eninfo:eu-repo/semantics/closedAccessCanal surfaceOsculating circleSurface of osculating circlesWeingarten surfaceArticle52119721010.1007/s10013-022-00585-0N/AWOS:0008546816000012-s2.0-85138100480