Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Cilt: 12 Sayı: 4, 169 - 177
https://doi.org/10.36753/mathenot.1481075

Öz

Kaynakça

  • [1] Hamilton,W. R.: Elements of Quaternions I, II and III. Chelsea, New York (1899).
  • [2] Bharathi, K., Nagaraj, M.:Quaternion valued function of a real variable Serret-Frenet formulaetext. Indian J. Pure Appl. Math. 16, 741-756 (1985).
  • [3] Tuna, A.: Serret Frenet formulae for quaternionic curves in semi Euclidean space. Ph.D. thesis. Süleyman Demirel University (2002).
  • [4] Kahraman Aksoyak, F.: A new type of quaternionic frame in R4. International Journal of Geometric Methods in Modern Physics. 16(06), 1950084 (2019).
  • [5] Çöken, A. C., Tuna, A.: On the quaternionic inclined curves in the semi-Euclidean space E4 2 . Appl. Math. Comput. 155, 373-389 (2004).
  • [6] Eren, K.: Motion of inextensible quaternionic curves and modified Korteweg-de Vries equation. Analeleştiintifice ale Universitatii" Ovidius" Constanta. Seria Matematica. 30(2), 91-101 (2022).
  • [7] Güngör, M. A., Erişir, T.:On the quaternionic curves in the semi-Euclidean space E4_2 . Caspian Journal of Mathematical Sciences (CJMS). 7(1), 36-45 (2018).
  • [8] Gök, İ., Okuyucu, O. Z., Kahraman, F., Hacısalihoğlu, H. H.: On the quaternionic B2 slant helices in the Euclidean space E4;. Adv.Appl. Clifford Algebras. 21, 707-719 (2011).
  • [9] Kahraman Aksoyak, F.: Quaternionic Bertrand curves according to type 2-quaternionic frame in R4. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 71(2), 395-406 (2022).
  • [10] Kızılay, A., Yıldız, Ö. G., Okuyucu, O. Z.:Evolution of quaternionic curve in the semi-Euclidean space E4_2 .Mathematical Methods in the Applied Sciences. 44(9), 7577-7587 (2021).
  • [11] Yıldız, Ö. G., Özkaldı Karakuş, S.:On the Quaternionic Normal Curves in the Semi-Euclidean Space E4 2 . International Journal of Mathematical Combinatorics. 3, 68-76 (2016).
  • [12] Yıldız, A. F., Okuyucu, O. Z., Yıldız, Ö. G.: Inextensible flow Of a semi-real quaternionic curve In semi-Euclidean space R4_2 . Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 67(1), 323-332 (2018).
  • [13] Kwon, D. Y., Park, F. C.: Evolution of inelastic plane curves. Applied Mathematics Letters. 12(6), 115-119 (1999).
  • [14] Kwon, D. Y., Park, F. C., Chi, D. P.: Inextensible flows of curves and developable surfaces. Applied Mathematics Letters. 18(10), 1156-1162 (2005).
  • [15] Eren, K.: A study of the evolution of space curves with modified orthogonal frame In Euclidean 3-space. Applied Mathematics E-Notes. 22, 281-286 (2022).
  • [16] Gün Bozok, H., Dostoğlu, O. T.: Inextensible flows of framed curves in 4-dimensional Euclidean space. Advanced Studies: Euro-Tbilisi Mathematical Journal. 16(4), 67-75 (2023).
  • [17] Kelleci, A., Eren, K.: On evolution of some associated type ruled surfaces. Math. Sci. Appl. E-Notes. 8(2), 178-186 (2020).
  • [18] Kızılay, A., Yakut, A. T.:Inextensible flows of space curves according to a new orthogonal frame with curvature in E3_ 1. International Electronic Journal of Geometry. 16(2), 577-593 (2023).
  • [19] Şenyurt, S., Eren, K., Ayvacı, K. H.: A study on inextensible flows of polynomial curves with Flc Frame. Applications and Applied Mathematics: An International Journal (AAM). 17(2), 123-133 (2022).
  • [20] Ward, J. P.: Quaternions and Cayley numbers: algebra and applications. Vol. 403. Springer Science and Business Media. (2012).

Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space

Yıl 2024, Cilt: 12 Sayı: 4, 169 - 177
https://doi.org/10.36753/mathenot.1481075

Öz

In this paper, we investigate inextensible flows of quaternionic curve according to Type 2-Quaternionic frame. We give necessary and sufficient conditions for inextensible flow of quaternionic curves. Moreover, we obtain evolution equations of the Frenet frame and curvatures according to Type 2-Quaternionic frame.

Kaynakça

  • [1] Hamilton,W. R.: Elements of Quaternions I, II and III. Chelsea, New York (1899).
  • [2] Bharathi, K., Nagaraj, M.:Quaternion valued function of a real variable Serret-Frenet formulaetext. Indian J. Pure Appl. Math. 16, 741-756 (1985).
  • [3] Tuna, A.: Serret Frenet formulae for quaternionic curves in semi Euclidean space. Ph.D. thesis. Süleyman Demirel University (2002).
  • [4] Kahraman Aksoyak, F.: A new type of quaternionic frame in R4. International Journal of Geometric Methods in Modern Physics. 16(06), 1950084 (2019).
  • [5] Çöken, A. C., Tuna, A.: On the quaternionic inclined curves in the semi-Euclidean space E4 2 . Appl. Math. Comput. 155, 373-389 (2004).
  • [6] Eren, K.: Motion of inextensible quaternionic curves and modified Korteweg-de Vries equation. Analeleştiintifice ale Universitatii" Ovidius" Constanta. Seria Matematica. 30(2), 91-101 (2022).
  • [7] Güngör, M. A., Erişir, T.:On the quaternionic curves in the semi-Euclidean space E4_2 . Caspian Journal of Mathematical Sciences (CJMS). 7(1), 36-45 (2018).
  • [8] Gök, İ., Okuyucu, O. Z., Kahraman, F., Hacısalihoğlu, H. H.: On the quaternionic B2 slant helices in the Euclidean space E4;. Adv.Appl. Clifford Algebras. 21, 707-719 (2011).
  • [9] Kahraman Aksoyak, F.: Quaternionic Bertrand curves according to type 2-quaternionic frame in R4. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 71(2), 395-406 (2022).
  • [10] Kızılay, A., Yıldız, Ö. G., Okuyucu, O. Z.:Evolution of quaternionic curve in the semi-Euclidean space E4_2 .Mathematical Methods in the Applied Sciences. 44(9), 7577-7587 (2021).
  • [11] Yıldız, Ö. G., Özkaldı Karakuş, S.:On the Quaternionic Normal Curves in the Semi-Euclidean Space E4 2 . International Journal of Mathematical Combinatorics. 3, 68-76 (2016).
  • [12] Yıldız, A. F., Okuyucu, O. Z., Yıldız, Ö. G.: Inextensible flow Of a semi-real quaternionic curve In semi-Euclidean space R4_2 . Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 67(1), 323-332 (2018).
  • [13] Kwon, D. Y., Park, F. C.: Evolution of inelastic plane curves. Applied Mathematics Letters. 12(6), 115-119 (1999).
  • [14] Kwon, D. Y., Park, F. C., Chi, D. P.: Inextensible flows of curves and developable surfaces. Applied Mathematics Letters. 18(10), 1156-1162 (2005).
  • [15] Eren, K.: A study of the evolution of space curves with modified orthogonal frame In Euclidean 3-space. Applied Mathematics E-Notes. 22, 281-286 (2022).
  • [16] Gün Bozok, H., Dostoğlu, O. T.: Inextensible flows of framed curves in 4-dimensional Euclidean space. Advanced Studies: Euro-Tbilisi Mathematical Journal. 16(4), 67-75 (2023).
  • [17] Kelleci, A., Eren, K.: On evolution of some associated type ruled surfaces. Math. Sci. Appl. E-Notes. 8(2), 178-186 (2020).
  • [18] Kızılay, A., Yakut, A. T.:Inextensible flows of space curves according to a new orthogonal frame with curvature in E3_ 1. International Electronic Journal of Geometry. 16(2), 577-593 (2023).
  • [19] Şenyurt, S., Eren, K., Ayvacı, K. H.: A study on inextensible flows of polynomial curves with Flc Frame. Applications and Applied Mathematics: An International Journal (AAM). 17(2), 123-133 (2022).
  • [20] Ward, J. P.: Quaternions and Cayley numbers: algebra and applications. Vol. 403. Springer Science and Business Media. (2012).
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm Articles
Yazarlar

Önder Gökmen Yıldız 0000-0002-2760-1223

Hazer Usta Bu kişi benim 0009-0001-7164-2137

Erken Görünüm Tarihi 16 Temmuz 2024
Yayımlanma Tarihi
Gönderilme Tarihi 9 Mayıs 2024
Kabul Tarihi 19 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 4

Kaynak Göster

APA Yıldız, Ö. G., & Usta, H. (2024). Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space. Mathematical Sciences and Applications E-Notes, 12(4), 169-177. https://doi.org/10.36753/mathenot.1481075
AMA Yıldız ÖG, Usta H. Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space. Math. Sci. Appl. E-Notes. Temmuz 2024;12(4):169-177. doi:10.36753/mathenot.1481075
Chicago Yıldız, Önder Gökmen, ve Hazer Usta. “Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space”. Mathematical Sciences and Applications E-Notes 12, sy. 4 (Temmuz 2024): 169-77. https://doi.org/10.36753/mathenot.1481075.
EndNote Yıldız ÖG, Usta H (01 Temmuz 2024) Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space. Mathematical Sciences and Applications E-Notes 12 4 169–177.
IEEE Ö. G. Yıldız ve H. Usta, “Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space”, Math. Sci. Appl. E-Notes, c. 12, sy. 4, ss. 169–177, 2024, doi: 10.36753/mathenot.1481075.
ISNAD Yıldız, Önder Gökmen - Usta, Hazer. “Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space”. Mathematical Sciences and Applications E-Notes 12/4 (Temmuz 2024), 169-177. https://doi.org/10.36753/mathenot.1481075.
JAMA Yıldız ÖG, Usta H. Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space. Math. Sci. Appl. E-Notes. 2024;12:169–177.
MLA Yıldız, Önder Gökmen ve Hazer Usta. “Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space”. Mathematical Sciences and Applications E-Notes, c. 12, sy. 4, 2024, ss. 169-77, doi:10.36753/mathenot.1481075.
Vancouver Yıldız ÖG, Usta H. Inextensible Flow of Quaternionic Curves According to Type 2-Quaternionic Frame in the Euclidean Space. Math. Sci. Appl. E-Notes. 2024;12(4):169-77.

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