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On the Special Viviani’s Curve and Its Corresponding Smarandache Curves

Author

Listed:
  • Yangke Deng

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

  • Yanlin Li

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

  • Süleyman Şenyurt

    (Department of Mathematics, Ordu University, Ordu 52200, Türkiye)

  • Davut Canlı

    (Department of Mathematics, Ordu University, Ordu 52200, Türkiye)

  • İremnur Gürler

    (Department of Mathematics, Ordu University, Ordu 52200, Türkiye)

Abstract

In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector. Then, it expresses the resulting Frenet apparatus for each Smarandache curve in terms of the Viviani’s curve. The paper is also supported by extensive graphical representations of Viviani’s curve and its Smarandache curves, as well as their respective curvatures.

Suggested Citation

  • Yangke Deng & Yanlin Li & Süleyman Şenyurt & Davut Canlı & İremnur Gürler, 2025. "On the Special Viviani’s Curve and Its Corresponding Smarandache Curves," Mathematics, MDPI, vol. 13(9), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1526-:d:1650040
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    References listed on IDEAS

    as
    1. Xin Zhao & Donghe Pei, 2021. "Evolutoids of the Mixed‐Type Curves," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    2. Xin Zhao & Donghe Pei, 2021. "Evolutoids of the Mixed-Type Curves," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-9, December.
    3. Yanlin Li & M. S. Siddesha & H. Aruna Kumara & M. M. Praveena, 2024. "Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds," Mathematics, MDPI, vol. 12(19), pages 1-11, October.
    4. Esra Betul Koc Ozturk & Ufuk Ozturk & Kazim İlarslan & Emilija Nešović, 2013. "On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-7, May.
    5. Yanlin Li & Mohamed Lemine H. Bouleryah & Akram Ali, 2024. "On Convergence of Toeplitz Quantization of the Sphere," Mathematics, MDPI, vol. 12(22), pages 1-15, November.
    Full references (including those not matched with items on IDEAS)

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