Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 15 Sayı: 1, 118 - 124, 30.06.2023
https://doi.org/10.47000/tjmcs.1141025

Öz

Kaynakça

  • Chen, B.Y., Ishikawa, S., Biharmonic surfaces in pseudo-Euclidean spaces, Mem. Fac. Sci. Kyushu Univ. Ser. A, 45 (1991), 323–347.
  • Chen, B.Y., On the total curvature of immersed manifolds, VI : Submanifolds of nite type and their applications, Bull. Ins. Math. Acad. Sinica, 11(1983), 309–328.
  • Çakmak, A., Şahin, V., Characterizations of adjoint curves according to alternative moving frame, Fundamental Journal of Mathematics and Applications, 5(1)(2022), 42–50.
  • Ferrandez, A., Lucas, P., Merono, M.A., Biharmonic Hopf cylinders, Rocky Mountain J., 28(1998), 957–975.
  • Inoguchi, J., Biharmonic curves in Minkowski 3-space, International J. Math. Sci., 21(2003), 1365-1368.
  • Inoguchi, J., Biharmonic curves in Minkowski 3-space part II, International J. of Math. and Mathematical Sci., (2006), Article ID 92349, 1–4.
  • Kilic, B., Finite Type Curves and Surfaces, Ph. Thesis, University of Hacettepe, 2002.
  • Kocayiğit, H., Hacısalihoğlu, H.H., 1-type and biharmonic curves in Euclidean 3-space, International Electronic Journal of Geometry , 4(2011), 97–101.
  • Körpınar, T., Turhan, E., Biharmonic curves according to parallel transport frame in $E^{4}$, Bol. Soc. Paran. Mat., 31(2)(2013), 213–217.
  • Külahcı, M., Biharmonic curves in isotropic space $I_{1}^{3}$ , Prespacetime Journal, 7(10)(2016), 1411–1415.
  • Ozturk, G., Bayram, B.K., Arslan, K., Weak biharmonic curve and harmonic 1-type curve in semi-Euclidean space $E_{1}^{4}$, Acta Universitatis Apulensis, 40(2014), 97–101.
  • Perktas¸, S.Y., Kılıç, E., On biharmonic curves in 3-dimensional Heisenberg group, Adıyaman University Journal of Science, 2(2)(2012), 58–74.
  • Uzunoğlu, B., Gök, I., Yaylı, Y., A new approach on curves of constant precession, Appl. Math. Comput. 275(2016), 317–323.

A New Approach on Some Special Curves

Yıl 2023, Cilt: 15 Sayı: 1, 118 - 124, 30.06.2023
https://doi.org/10.47000/tjmcs.1141025

Öz

In this paper, we obtain some characterizations for a Frenet curve with the help of an alternative frame different from Frenet frame. Also, in the present study we consider weak biharmonic and harmonic 1-type curves by using the mean curvature vector field of the curve. We also study 1-type and biharmonic curves whose mean curvature vector field is in the kernel of Laplacian. We give some theorems for them in the Euclidean 3-space. Moreover, we give the classifications of these type curves.

Kaynakça

  • Chen, B.Y., Ishikawa, S., Biharmonic surfaces in pseudo-Euclidean spaces, Mem. Fac. Sci. Kyushu Univ. Ser. A, 45 (1991), 323–347.
  • Chen, B.Y., On the total curvature of immersed manifolds, VI : Submanifolds of nite type and their applications, Bull. Ins. Math. Acad. Sinica, 11(1983), 309–328.
  • Çakmak, A., Şahin, V., Characterizations of adjoint curves according to alternative moving frame, Fundamental Journal of Mathematics and Applications, 5(1)(2022), 42–50.
  • Ferrandez, A., Lucas, P., Merono, M.A., Biharmonic Hopf cylinders, Rocky Mountain J., 28(1998), 957–975.
  • Inoguchi, J., Biharmonic curves in Minkowski 3-space, International J. Math. Sci., 21(2003), 1365-1368.
  • Inoguchi, J., Biharmonic curves in Minkowski 3-space part II, International J. of Math. and Mathematical Sci., (2006), Article ID 92349, 1–4.
  • Kilic, B., Finite Type Curves and Surfaces, Ph. Thesis, University of Hacettepe, 2002.
  • Kocayiğit, H., Hacısalihoğlu, H.H., 1-type and biharmonic curves in Euclidean 3-space, International Electronic Journal of Geometry , 4(2011), 97–101.
  • Körpınar, T., Turhan, E., Biharmonic curves according to parallel transport frame in $E^{4}$, Bol. Soc. Paran. Mat., 31(2)(2013), 213–217.
  • Külahcı, M., Biharmonic curves in isotropic space $I_{1}^{3}$ , Prespacetime Journal, 7(10)(2016), 1411–1415.
  • Ozturk, G., Bayram, B.K., Arslan, K., Weak biharmonic curve and harmonic 1-type curve in semi-Euclidean space $E_{1}^{4}$, Acta Universitatis Apulensis, 40(2014), 97–101.
  • Perktas¸, S.Y., Kılıç, E., On biharmonic curves in 3-dimensional Heisenberg group, Adıyaman University Journal of Science, 2(2)(2012), 58–74.
  • Uzunoğlu, B., Gök, I., Yaylı, Y., A new approach on curves of constant precession, Appl. Math. Comput. 275(2016), 317–323.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Tuba Ağırman Aydın 0000-0001-8034-0723

Hüseyin Kocayiğit 0000-0001-6503-8243

Yayımlanma Tarihi 30 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 15 Sayı: 1

Kaynak Göster

APA Ağırman Aydın, T., & Kocayiğit, H. (2023). A New Approach on Some Special Curves. Turkish Journal of Mathematics and Computer Science, 15(1), 118-124. https://doi.org/10.47000/tjmcs.1141025
AMA Ağırman Aydın T, Kocayiğit H. A New Approach on Some Special Curves. TJMCS. Haziran 2023;15(1):118-124. doi:10.47000/tjmcs.1141025
Chicago Ağırman Aydın, Tuba, ve Hüseyin Kocayiğit. “A New Approach on Some Special Curves”. Turkish Journal of Mathematics and Computer Science 15, sy. 1 (Haziran 2023): 118-24. https://doi.org/10.47000/tjmcs.1141025.
EndNote Ağırman Aydın T, Kocayiğit H (01 Haziran 2023) A New Approach on Some Special Curves. Turkish Journal of Mathematics and Computer Science 15 1 118–124.
IEEE T. Ağırman Aydın ve H. Kocayiğit, “A New Approach on Some Special Curves”, TJMCS, c. 15, sy. 1, ss. 118–124, 2023, doi: 10.47000/tjmcs.1141025.
ISNAD Ağırman Aydın, Tuba - Kocayiğit, Hüseyin. “A New Approach on Some Special Curves”. Turkish Journal of Mathematics and Computer Science 15/1 (Haziran 2023), 118-124. https://doi.org/10.47000/tjmcs.1141025.
JAMA Ağırman Aydın T, Kocayiğit H. A New Approach on Some Special Curves. TJMCS. 2023;15:118–124.
MLA Ağırman Aydın, Tuba ve Hüseyin Kocayiğit. “A New Approach on Some Special Curves”. Turkish Journal of Mathematics and Computer Science, c. 15, sy. 1, 2023, ss. 118-24, doi:10.47000/tjmcs.1141025.
Vancouver Ağırman Aydın T, Kocayiğit H. A New Approach on Some Special Curves. TJMCS. 2023;15(1):118-24.