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Framed Natural Mates of Framed Curves in Euclidean 3-Space

Author

Listed:
  • Yanlin Li

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
    Key Laboratory of Cryptography of Zhejiang Province, Hangzhou Normal University, Hangzhou 311121, China)

  • Mahmut Mak

    (Department of Mathematics, Kırşehir Ahi Evran University, Kırşehir 40100, Turkey)

Abstract

In this study, we consider framed curves as regular or singular space curves with an adapted frame in Euclidean 3-space. We define framed natural mates of a framed curve that are tangent to the generalized principal normal of the framed curve. Subsequently, we present the relationships between a framed curve and its framed natural mates. In particular, we establish some necessary and sufficient conditions for the framed natural mates of specific framed curves, such as framed spherical curves, framed helices, framed slant helices, and framed rectifying curves. Finally, we support the concept with some examples.

Suggested Citation

  • Yanlin Li & Mahmut Mak, 2023. "Framed Natural Mates of Framed Curves in Euclidean 3-Space," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3571-:d:1219567
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    References listed on IDEAS

    as
    1. Yongqiao Wang & Donghe Pei & Ruimei Gao, 2019. "Generic Properties of Framed Rectifying Curves," Mathematics, MDPI, vol. 7(1), pages 1-12, January.
    2. Erol Kılıç & Mehmet Gülbahar & Ecem Kavuk, 2020. "Concurrent Vector Fields on Lightlike Hypersurfaces," Mathematics, MDPI, vol. 9(1), pages 1-16, December.
    3. Miroslava Antić & Djordje Kocić, 2022. "Non-Existence of Real Hypersurfaces with Parallel Structure Jacobi Operator in S 6 (1)," Mathematics, MDPI, vol. 10(13), pages 1-12, June.
    4. Yanlin Li & Sujit Bhattacharyya & Shahroud Azami & Apurba Saha & Shyamal Kumar Hui, 2023. "Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    5. Engin As & Süleyman Şenyurt, 2013. "Some Characteristic Properties of Parallel -Equidistant Ruled Surfaces," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, June.
    Full references (including those not matched with items on IDEAS)

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