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

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  • Azeb Alghanemi
  • Abeer AlGhawazi
  • Meraj Ali Khan

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.

Suggested Citation

  • Azeb Alghanemi & Abeer AlGhawazi & Meraj Ali Khan, 2022. "Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-9, April.
    • Handle: RePEc:hin:jnlamp:9881237
    DOI: 10.1155/2022/9881237
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    Cited by:

    1. Azeb Alghanemi & Abeer AlGhawazi, 2023. "The λ -Point Map between Two Legendre Plane Curves," Mathematics, MDPI, vol. 11(4), pages 1-9, February.

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