Canal Surfaces Through a Null Quaternionic Spine Curve

Gül TUĞ (Karadeniz Teknik Üniversitesi, Matematik Bölümü, Trabzon, Türkiye)
Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi
3 0
Yıl: 2022 Cilt: 9 Sayı: 2 Sayfa Aralığı: 721 - 729 Metin Dili: İngilizce DOI: 10.35193/bseufbd.1059044 İndeks Tarihi: 11-01-2023

Canal Surfaces Through a Null Quaternionic Spine Curve

Öz:
In this study, we give the parameterizations of the canal surfaces through a null quaternionic spine curve by using the pseudo-spheres in ℝ𝟏𝟒. Besides, we give formulas for the Gauss and Mean curvatures and some corollaries related to the Cartan curvatures of the null quaternionic curve.
Anahtar Kelime:

Null Kuaterniyonik Omurga Eğrisi Boyunca Kanal Yüzeyler

Öz:
Bu çalışmada, ℝ𝟏 𝟒 deki pseudo-küreleri kullanarak, bir null kuaterniyonik omurga eğrisi boyunca kanal yüzeylerin parametrizasyonları verilmiştir. Ayrıca, Gauss ve ortalama eğrilikler hesaplanmış ve null kuaterniyonik eğrinin Cartan eğrilikleri ile ilişkili bazı sonuçlar elde edilmiştir.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Hamilton, W. R. (1844). On quaternions; or on a new system of imagniaries in algebra. Lond. Edinb. Dublin. Philos. Mag. J. Sci., 25 (3), 489-495.
  • [2] Aslan, S & Yaylı, Y. (2016). Canal surfaces with quaternions. Adv. Appl. Cliffor.d Algebras, 26, 31–8.
  • [3] Gök, İ. (2017). Quaternionic approach of canal surfaces constructed by some new ideas. Adv. Appl. Clifford Algebras, 27, 1175-1190.
  • [4] Shoemake, K. (1985). Animating rotation with quaternion curves. Proceedings of the 12th annual conference on computer graphics and interactive techniques (SIG-GRAPH 85), 19, New York, NY, USA, 245-254.
  • [5] Haralick, R. M. (2017). Longitudinal & Scalar Waves: Biquaternion generalized maxwell equations. Computer Science, Graduate Center, 172.
  • [6] Rosenfeld, B. (1997). Geometry of Lie groups. Kluwer Academic Publishers, Netherlands, 397.
  • [7] Dyachkova, M. (2007). On Hopf bundle analogue for semiquaternion algebra. 10th International Conference DGA, Olomouc, Czech Republic, 45-47.
  • [8] Bharathi, K. & Nagaraj, M. (1987). Quaternion valued function of a real variable Serret-Frenet formula. Indian J. Pure Appl. Math., 18, 507-511.
  • [9] Çöken, A. C. & Tuna, A. (2004). On the quaternionic inclined curves in the semi-Euclidean space E42. Appl. Math. Comput., 155, 373–389.
  • [10] Gök, İ., Okuyucu, O. Z., Kahraman, F. & Hacisalihoglu, H. H. (2011). On the quaternionic B2-slant helix in the Euclidean space E4. Adv. Appl. Clifford Algebras, 21, 707–719.
  • [11] Körpınar, T. & Baş, S. (2016). Characterization of Quaternionic Curves by Inextensible Flows. Prespacetime Journal, 7, 1680-1684.
  • [12] Okuyucu, O. Z. (2013). Characterizations of the quaternionic Mannheim curves in Euclidean space E4. Mathematical Combinatorics, 2, 44-53.
  • [13] Kecilioglu, O. & Ilarslan, K. (2013). Quaternionic Bertrand Curves in Euclidean 4-Space. Bull. Math. Anal. Appl., 5 (3), 27-38.
  • [14] Önder, M. (2020). Quaternionic Salkowski Curves and Quaternionic Similar Curves. Proc. Natl. Acad. Sci. India, Sect. A Phys. Sci., 90 (3), 447-456.
  • [15] Shoemake, K . (1985). Animating rotation with quaternion curves. Proceedings of the 12th annual conference on computer graphics and interactive techniques (SIG-GRAPH 85), 19, New York, NY, USA, 245-254 .
  • [16] Duggal, K. L. & Bejancu, A. (1996), Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic Publisher, Dordrecht / Boston / London, 303.
  • [17] Ferrandez A., Gimenez A. & Lucas P. (2001). Null Helices in Lorentzian Space Forms. Int. J. Mod. Phys. A, 16 (30), 4845-4863.
  • [18] Çoken, A. C. & Ciftci, U. (2005). On the Cartan curvatures of a null curve in Minkowski spacetime. Geom. Dedicata, 114, 71-78.
  • [19] Kahraman, T. (2019). Null Quaternionic Slant Helices in Minkowski Spaces. International J.Math. Combin., 1, 45-52.
  • [20] Aksoy, A. T. (2016). Pseudo-Spherical Null Quaternionic Curves in Minkowski Space 𝑅4. Acta Physica Polonica A, 130, 259-261.
  • [21] Özel, Ş., Külahçı, M. A. & Bektaş, M. (2021). The Characterizations Of Null Quaternionic Curves In Minkowski 3-Space. Turkish Journal of Science and Technology, 16 (2), 261-267.
  • [22] Aksoy, A. T. & Çöken, A. C. (2015). Null Quaternionic Curves in Semi-Euclidean 3-Space of Index 𝜈. Acta Physica Polonica A, 128, B-286-B-289.
  • [23] Maekawa, T., Patrikalakis, M. N., Sakkalis, T. & Yu, G. (1998). Analysis and applications of pipe surfaces. Comput. Aided Geom. Des., 15, 437–58 .
  • [24] Shani, U. & Ballard, D. H. (1984). Splines as embeddings for generalized cylinders. Computer Vision , Graphics and Image Processing, 27, 129-156.
  • [25] Wang, L., Ming, C. L. & Blackmore, D. (1995). Generating sweep solids for NC verification using the SEDE method. Proceedings of the Fourth Symposium on Solid Modeling and Applications, Atlanta, 364- 375.
  • [26] Farouki, R. T. & Sverrissor, R. (1996). Approximation of rolling-ball blends for free-form parametric surfaces. Computer-Aided Design, 28, 871-878.
  • [27] Xu, Z., Feng, R. & Sun, JG. (2006). Analytic and algebraic properties of canal surfaces. Journal of Computational and Applied Mathematics, 195 (1-2), 220-228.
  • [28] Jinhua Qian, J., Tian, X., Fu, X. & Kim, Y. H. (2020). Classifications of Canal Surfaces with the Gauss Maps in Minkowski 3-Space. Mathematics, 8, 1453.
  • [29] Gray, A., Abbana, E. & Salamon, S. (2006). Modern Differential Geometry of Curves and Surfaces with Mathematica (3rd edition), Studies in Advanced Mathematics, Chapman and Hall/CRC, Boca Raton, FL, 1016.
  • [30] Ates, F. (2021). Tubular Surfaces Around a Null Curve and Its Spherical Images, FUJMA, 4 (3), 210-220.
APA Tuğ G (2022). Canal Surfaces Through a Null Quaternionic Spine Curve. , 721 - 729. 10.35193/bseufbd.1059044
Chicago Tuğ Gül Canal Surfaces Through a Null Quaternionic Spine Curve. (2022): 721 - 729. 10.35193/bseufbd.1059044
MLA Tuğ Gül Canal Surfaces Through a Null Quaternionic Spine Curve. , 2022, ss.721 - 729. 10.35193/bseufbd.1059044
AMA Tuğ G Canal Surfaces Through a Null Quaternionic Spine Curve. . 2022; 721 - 729. 10.35193/bseufbd.1059044
Vancouver Tuğ G Canal Surfaces Through a Null Quaternionic Spine Curve. . 2022; 721 - 729. 10.35193/bseufbd.1059044
IEEE Tuğ G "Canal Surfaces Through a Null Quaternionic Spine Curve." , ss.721 - 729, 2022. 10.35193/bseufbd.1059044
ISNAD Tuğ, Gül. "Canal Surfaces Through a Null Quaternionic Spine Curve". (2022), 721-729. https://doi.org/10.35193/bseufbd.1059044
APA Tuğ G (2022). Canal Surfaces Through a Null Quaternionic Spine Curve. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 9(2), 721 - 729. 10.35193/bseufbd.1059044
Chicago Tuğ Gül Canal Surfaces Through a Null Quaternionic Spine Curve. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 9, no.2 (2022): 721 - 729. 10.35193/bseufbd.1059044
MLA Tuğ Gül Canal Surfaces Through a Null Quaternionic Spine Curve. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, vol.9, no.2, 2022, ss.721 - 729. 10.35193/bseufbd.1059044
AMA Tuğ G Canal Surfaces Through a Null Quaternionic Spine Curve. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2022; 9(2): 721 - 729. 10.35193/bseufbd.1059044
Vancouver Tuğ G Canal Surfaces Through a Null Quaternionic Spine Curve. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2022; 9(2): 721 - 729. 10.35193/bseufbd.1059044
IEEE Tuğ G "Canal Surfaces Through a Null Quaternionic Spine Curve." Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 9, ss.721 - 729, 2022. 10.35193/bseufbd.1059044
ISNAD Tuğ, Gül. "Canal Surfaces Through a Null Quaternionic Spine Curve". Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 9/2 (2022), 721-729. https://doi.org/10.35193/bseufbd.1059044
Sayfa Oluşturulma Tarihi
24-04-2024 5:32

İLETİŞİM

TÜBİTAK ULAKBİM TR Dizin

Yüzüncüyıl, İşçi Blokları Mahallesi

Muhsin Yazıcıoğlu Caddesi No:51/C

06530 Çankaya / ANKARA +90 (312) 298 92 00

trdizin@tubitak.gov.tr

TÜBİTAK ULAKBİM Ulusal Akademik Ağ ve Bilgi Merkezi Cahit Arf Bilgi Merkezi © Tüm Hakları Saklıdır. Gizlilik Politikası Kullanım Şartları