Framed general helix and framed ζ3-slant helix in ℝ4

Ateş, Mine; Akyiğit, Mahmut

doi:10.2478/auom-2023-0029

Abstract

In this paper, we focus on general and ζ₃-slant helices with any singular points in four-dimensional Euclidean space, which are called framed general and ζ₃-slant helices, respectively. Then, we state and prove the conditions of necessity and su ciency for any framed curves to be general helices or ζ₃-slant helices in ℝ⁴. Also, we give some characterizations for framed helices.

References

Akyiğit, M., Yıldız, Ö.G., On the Framed Normal Curves in Euclidean 4-Space. Fundam. J. Math. Appl., 4(4) (2021), 258-263.
Search in Google Scholar Back to article
Honda, S., Flat surfaces associated with framed base curves, Doctoral Thesis, Hokkaido University, 2018.
Search in Google Scholar Back to article
Izumiya, S., Takeuchi, N., New Special Curves and Developable Surfaces. Turkish J. Math., 28(2) (2004), 153-164.
Search in Google Scholar Back to article
Kazaz, M., Önder, M., Kocayiğit, H., Kılıç, O., B2-Slant Helices in the Euclidean 4-Space. Int. J. Contemp. Math. Sciences, 3(29) (2008), 1433-1440.
Search in Google Scholar Back to article
Kula, L., Altunkaya, B., General helices that lie on the sphere S2n in Euclidean space E2n+1. Univers. J. Math. Appl., 1(3) (2018), 166-170.
Search in Google Scholar Back to article
Kula, L., Altunkaya, B., Characterizations of slant and spherical helices due to pseudo-Sabban frame. Fundam. J. Math. Appl., 1(1) (2018), 49-56.
Search in Google Scholar Back to article
Lancret, M.A., Mémoire sur la théorie des courbes á double courbure. Mémoires présentés à lInstitut des Sciences, Letters et arts par divers savants, 1 (1806), 416-454.
Search in Google Scholar Back to article
Mağden, A., On the curves of constant slope. YYÜ Fen Bilimleri Dergisi, 4 (1993), 103-109.
Search in Google Scholar Back to article
Okuyucu, O.Z., Canbirdi, M., Framed slant helices in Euclidean 3-space. Adv. Di erence Equ., 1 (2021), 1-14.
Search in Google Scholar Back to article
Özdoğan, S., Tuncer, O.O., Gök, İ., Yaylı, Y., Some new types of associated curves in Euclidean 3-space. Analele Stiintifice ale Univ. Ovidius Constanta, Ser. Mat., 26 (2018), 205-221.
Search in Google Scholar Back to article
Struik, D.J., Lectures on Classical Di erential Geometry. Int. J. Open Problems Compt. Math., Dover, New-York, 1988. MR 89b:53002
Search in Google Scholar Back to article
Wang, Y., Pei, D., Gao, R., Generic Properties of Framed Rectifying Curves. Mathematics, 7(1) (2019), 37.
Search in Google Scholar Back to article
Yıldız, Ö.G., On the evolution of framed curves in Euclidean 3-space. Math. Methods Appl. Sci. (2021). https://doi.org/10.1002/mma.7633
Search in Google Scholar Back to article
Yoon, D.W., On the Quaternionic General Helices in Euclidean 4-space. Honam Mathematical J., 34(3) (2012), 381-390.
Search in Google Scholar Back to article
Yazıcı, B.D., Özkaldı Karakuş, S., Tosun, M., Characterizations of Framed Curves in Four-Dimensional Euclidean Space. Univ. J. Math. Appl., 4(4) (2021), 125-131.
Search in Google Scholar Back to article

Framed general helix and framed ζ3-slant helix in ℝ4

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