Surfaces of Osculating Circles in Euclidean Space

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López R., CAMCI Ç., Uçum A., Ilarslan K.

Vietnam Journal of Mathematics, vol.52, no.1, pp.197-210, 2024 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1007/s10013-022-00585-0
  • Journal Name: Vietnam Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.197-210
  • Keywords: Osculating circle, Surface of osculating circles, Canal surface, Weingarten surface, TRANSLATION SURFACES, CURVES
  • Çanakkale Onsekiz Mart University Affiliated: Yes


© 2022, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.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.