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Journals / International Electronic Journal of Geometry / 2023 / Volume: 16 Issue: 2

A New Insight on Rectifying-Type Curves in Euclidean 4-Space

Zehra İşbilir(DUZCE UNIVERSITY, FACULTY OF ARTS AND SCIENCES)0000-0001-5414-5887
Murat Tosun(SAKARYA UNIVERSITY)0000-0002-4888-1412
Pages
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Publication Date
2023-10-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Additionally, we obtain an illustrative example with respect to the rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, our purpose is to determine the generalized rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$.
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Key Findings & Data:Also, some characterizations of them are given.
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Conclusion & Impact:Additionally, we obtain an illustrative example with respect to the rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Myller configuration · generalized rectifying type curves · four-dimensional space

Abstract

In this study, our purpose is to determine the generalized rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$. Also, some characterizations of them are given. We construct some correlations between curvatures and invariants of generalized rectifying-type curves. Additionally, we obtain an illustrative example with respect to the rectifying-type curves with Frenet-type frame in Myller configuration for Euclidean 4-space $E_4$.

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Cite This Article

İşbilir, Z., Tosun, M. (2023). A New Insight on Rectifying-Type Curves in Euclidean 4-Space. International Electronic Journal of Geometry, Volume: 16 Issue: 2. https://doi.org/10.36890/iejg.1291893

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References (52)

  1. Akyiğit, M., Yıldız, Ö. G.: On the framed normal curves in Euclidean 4-space. Fundam. J. Math. Appl. 4 (4), 258–263 (2021).
  2. Breuer, S., Gottlieb, D.: Explicit characterization of spherical curves. Proc. Amer. Math. Soc. 27 (1), 126–127 (1971).
  3. Chen, B.-Y.: When does the position vector of a space curve always lie in its rectifying plane? Amer. Math. Monthly. 110 (2), 147–152 (2003).
  4. Chen, B.-Y.: Rectifying curves and geodesics on a cone in the Euclidean 3-space, Tamkang J. Math. 48 (2), 209-–214 (2017).
  5. Chen, B.-Y., Dillen, F.: Rectifying curves as centrodes and extremal curves. Bull. Inst. Math. Academia Sinica. 33 (2), 77–90 (2005).
  6. Constantinescu, O.: Myller configurations in Finsler spaces. Differential Geometry-Dynamical Systems. 8, 69–76 (2006).
  7. Deshmukh, S., Chen, B.-Y., Alshammari, S. H.: On rectifying curves in Euclidean 3-space. Turk. J. Math. 42 (2), 609-–620 (2018).
  8. Doğan Yazıcı, B., Özkaldı Karaku¸s, S., Tosun, M.: Characterizations of framed curves in four-dimensional Euclidean space. Univers. J. Math. Appl. 4 (4), 125–131 (2021).
  9. Gökçelik, F., Bozkurt, Z., Gök, İ, Ekmekçi, F. N., Yaylı, Y.: Parallel transport frame in 4-dimensional Euclidean space. Caspian J. Math. Sci. 3 (1), 91–103 (2014).
  10. Gluck, H.: Higher curvatures of curves in Euclidean space. Amer. Math. Monthly. 73, 699–704 (1966).
  11. Heroiu, B.: Versor fields along a curve in a four dimensional Lorentz space. J. Adv. Math. Stud. 4 (1), 49–57 (2011).
  12. İlarslan, K.: Spacelike normal curves in Minkowski space E31. Turk. J. Math. 29 (2), 53–63 (2005).
  13. İlarslan, K., Nešovic, E.: Spacelike and timelike normal curves in Minkowski space-time. Publications de l’Institut Mathmatique. 85 (99), 111–118 (2009).
  14. İlarslan, K., Nešovic, E.: Some characterizations of rectifying curves in Euclidean 4-spaces E4. Turk. J. Math. 32, 21–30 (2008).
  15. İlarslan, K., Nešovic, E.: Some characterizations of osculating curves in the Euclidean spaces. Demonstratio Mathematica. 41 (4), 931–940 (2008).
  16. İlarslan, K., Nešovic, E.: The first kind and the second kind osculating curves in Minkowski space-time. Compt. Rend. Acad. Bulg. Sci. 62 (6), 677–686 (2009).
  17. İlarslan, K., Nešovic, E., Petrovic–Torgašev, M.: Some characterizations of rectifying curves in the Minkowski 3–space. Novi Sad J. Math. 33 (2), 23-–32 (2003).
  18. İlarslan, K., Nešovic, E.: Timelike and null normal curves in Minkowski space E31. Indian J. Pure Appl. Math. 35 (7), 881–888 (2004).
  19. İlarslan, K., Nešovic, E.: Some characterizations of null, pseudo null and partially null rectifying curves in Minkowski space-time. Taiwan. J. Math. 12 (5), 1035–1044 (2008).
  20. 20] İlarslan, K., Nešovic, E.: Spacelike and timelike normal curves in Minkowski space-time. Publications de l’Institut Mathématique. 85 (99), 111–118 (2009).
  21. İlarslan, K., Nešovi´c, E.: Some characterizations of pseudo and partially null osculating curves in Minkowski space-time. Int. Electron. J. Geom. 4 (2), 1–12 (2011).
  22. İlarslan, K., Nešovic, E.: On rectifying curves as centrodes and extremal curves in the Minkowski 3-space. Novi Sad J. Math. 37 (1), 53–64 (2007).
  23. İşbilir, Z., Tosun, M.: On generalized osculating-type curves in Myller configuration. An. Şt. Univ. Ovidius Constanta, Ser. Mat. XXXII (2), (2024).
  24. İşbilir, Z., Tosun, M.: An extended framework for osculating-type curves in four-dimensional Euclidean space. (2023) (submitted).
  25. Keskin, Ö., Yaylı, Y.: Rectifying-type curves and rotation minimizing frame Rn. arXiv preprint, (2019). https://doi.org/10.48550/ arXiv.1905.04540.
  26. Kişi, ˙I.: Some characterizations of canal surfaces in the four dimensional Euclidean space, Ph.D. Thesis, Kocaeli University, (2018).
  27. Kuhnel, W.: Differential Geometry: Curves-Surfaces-Manifolds, Braunschweig, Wiesbaden (1999).
  28. Levi-Civita, T.: Rendiconti del Circolo di Palermo. (XLII), 173 (1917).
  29. Levi-Civita, T.: Lezioni di calcolo differentiate assoluto, Zanichelli, (1925).
  30. Macsim, G., Mihai, A., Olteanu, A.: Curves in a Myller configuration. International Conference on Applied and Pure Mathematics (ICAPM 2017), Iaşi, November 2-5, 2017.
  31. Macsim, G., Mihai, A., Olteanu, A.: On rectifying-type curves in a Myller configuration. Bull. Korean Math. Soc. 56 (2), 383–390 (2019).
  32. Macsim, G., Mihai, A., Olteanu, A.: Special curves in a Myller configuration. Proceedings of the 16th Workshop on Mathematics, Computer Science and Technical Education, Department of Mathematics and Computer Science, Volume 2, (2019).
  33. Miron, R.: The Geometry of Myller Configurations. Applications to Theory of Surfaces and Nonholonomic Manifolds, Romanian Academy, (2010).
  34. Miron, R.: Geometria unor configuratii Myller. Analele ¸St. Univ. VI (3), (1960).
  35. Miron, R.: Myller configurations and Vranceanu nonholonomic manifolds. Scientific Studies and Research. 21 (1), (2011).
  36. Miron, R.: Configura¸tii Myller M(C, ξi1, Tn−1) în spa¸tii Riemann Vn, Aplica¸tii la studiul hipersuprafe¸telor din Vn. Studii şi Cerc. Şt. Mat. Iaşi. XII (1), (1962).
  37. Miron, R.: Configuratii Myller M(C, ξ1 i, Tm) în spa¸tii Riemann Vn. Aplica¸tii la studiul varietˇa¸tilor Vm din Vn. Studii ¸si Cerc. St. Mat. Ia¸si. XIII (1), (1962).
  38. Miron, R.: Les configurations de MyllerM(C, ξ1i, Tn−1) dans les espaces de Riemann Vn (I). Tensor. 12 (3), (1962) (Japonia).
  39. Miron, R.: Les configurations de MyllerM(C, ξi1, Tm) dans les espaces de Riemann Vn. Tensor. V (1), (1964) (Japonia).
  40. Miron, R., Pop, I.: Topologie algebricˇa: omologie, omotopie, spa¸tii de acoperire. Ed. Academiei, (1974).
  41. Miron, R., Branzei, D.: Backgrounds of arithmetic and geometry, World Scientific Publishing, S. Pure Math. 23, (1995).
  42. Miron, R.: Geometria Configura¸tiilor Myller. Editura Tehnicˇa. Bucure¸sti (1966).
  43. Otsuki, T.: Differential Geometry. Asakura Pulishing Co. Ltd. Tokyo (1961).
  44. Vaisman, I.: Simplectic Geometry and Secondary Characteristic Classes. Progress in Mathematics. 72, Birkhauser Verlag, Basel (1994).
  45. Wong, Y. C.: A global formulation of the condition for a curve to lie in a sphere. Monatschefte fur Mathematik. 67, 363–365 (1963).
  46. Wong, Y. C.: On an explicit characterization of spherical curves. Proceedings of the American Math. Soc. 34 (1), 239–242 (1972).
  47. İlarslan, K.: Spacelike normal curves in Minkowski space E31. Turk. J. Math. 29 (2), 53–63 (2005).
  48. İlarslan, K., Nešovic, E., Petrovic–Torgašev, M.: Some characterizations of rectifying curves in the Minkowski 3–space. Novi Sad J. Math. 33 (2), 23-–32 (2003).
  49. İlarslan, K., Nešovic, E.: Timelike and null normal curves in Minkowski space E31. Indian J. Pure Appl. Math. 35 (7), 881–888 (2004).
  50. İlarslan, K., Nešovic, E.: On rectifying curves as centrodes and extremal curves in the Minkowski 3-space. Novi Sad J. Math. 37 (1), 53–64 (2007).
  51. Miron, R.: Configuratii Myller M(C, ξ1 i, Tm) în spa¸tii Riemann Vn. Aplica¸tii la studiul varietˇa¸tilor Vm din Vn. Studii ¸si Cerc. St. Mat. Ia¸si. XIII (1), (1962).
  52. Miron, R.: Les configurations de MyllerM(C, ξ1i, Tn−1) dans les espaces de Riemann Vn (I). Tensor. 12 (3), (1962) (Japonia).