Some Geometric Characterizations of f‐Curves Associated with a Plane Curve via Vector Fields

Azeb Alghanemi and Abeer AlGhawazi

Advances in Mathematical Physics, 2022, vol. 2022, issue 1

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.

Date: 2022
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https://doi.org/10.1155/2022/9881237

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:9881237

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