KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 17 Issue: 1

Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs

Yun Myung Oh(Andrews University)0000-0002-6526-8863
Alexander Navarro(Andrews University)0000-0003-3545-1891
Sayfa
—
Yayın Tarihi
2024-04-23
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate.
📊
Temel Bulgular & Veri:In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate.
💡
Sonuç & Katkı:A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Natual mates · co-successor curves · Bertrand curves

Abstract

In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate. A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.

🔖

Bu Makaleye Atıf Yap

Oh, Y. M., Navarro, A. (2024). Extending Natural Mates in Euclidean 3-space and Applications to Bertrand Pairs. International Electronic Journal of Geometry, Volume: 17 Issue: 1. https://doi.org/10.36890/iejg.1438073

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (8)

  1. Alghanemi, A., Khan, M.A.: Position Vectors of the Natural Mate and Conjugate of a Space Curve. Adv. Math. Phys., 1-5 (2023). https://doi.org/10.1155/2023/7565988
  2. Bertrand, J.M.: M’emoire sur la th’eorie des courbes a’ double courbure. Comptes Rendus. 15 (1), 332-350 (1850).
  3. Camci, Ç., Chen, B.-Y., ˙Ilarslan, K. et al.: Sequential natural mates of Frenet curves in Euclidean 3-space. J. Geom. 112, 46 (2021). https://doi.org/10.1007/s00022-021-00610-6
  4. Chen, B.-Y.: When does the position vector of a space curve always lie in its rectifying plane?. Amer. Math. Monthly. 110, 147-152 (2003).
  5. Choi, J. H., Kim, Y. H.: Associated curves of a Frenet curve and their applications. Appl. Math. Comput. 218 (18), 9116-9124 (2012). https://doi.org/10.1016/j.amc.2012.02.064
  6. Deshmukh S., Chen B.-Y., Alghanemi A.: Natural mates of Frenet curves in Euclidean 3-space. Turk. J. Math. 42, 2826–2840 (2018).
  7. Deshmukh, S., Chen B.-Y., Turki N.B.: A differential equations for Frenet curves in Euclidean 3-space and its applications. Rom. J. Math. Comput. Sci. 8, 1-6 (2018).
  8. Menninger, T.: Characterization of the slant helix as successor curve of the general helix. Int. Electron. J. Geom. 7, 84-91 (2014).