Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields. (27th April 2022)

• Record Type: Journal Article
• Authors: Alghanemi, Azeb; AlGhawazi, Abeer
• Other Names: Khan Meraj Ali Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2022(2022)
• Publication Date: 2022-04-27
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2022/9881237
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : The differential geometry of plane curves has many applications in physics especially in mechanics. The curvature of a plane curve plays a role in the centripetal acceleration and the centripetal force of a particle traversing a curved path in a plane. In this paper, we introduce the concept of the f -curves associated with a plane curve which are more general than the well-known curves such as involute, evolute, parallel, symmetry set, and midlocus. In fact, we introduce the f -curves associated with a plane curve via its normal and tangent for both the cases, a Frenet curve and a Legendre curve. Moreover, the curvature of an f -curve has been obtained in several approaches.