Surfaces of Osculating Circles in Euclidean Space
Vietnam Journal of Mathematics, cilt.52, sa.1, ss.197-210, 2024 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 52 Sayı: 1
- Basım Tarihi: 2024
- Doi Numarası: 10.1007/s10013-022-00585-0
- Dergi Adı: Vietnam Journal of Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, MathSciNet, zbMATH
- Sayfa Sayıları: ss.197-210
- Anahtar Kelimeler: Osculating circle, Surface of osculating circles, Canal surface, Weingarten surface, TRANSLATION SURFACES, CURVES
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Çanakkale Onsekiz Mart Üniversitesi Adresli: Evet
Özet
© 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.