On the evolute offsets of ruled surfaces using the Darboux frame

Gülsüm Yeliz Şentürk; Salim Yüce

doi:10.31801/cfsuasmas.516604

Araştırma Makalesi

On the evolute offsets of ruled surfaces using the Darboux frame

Yıl 2019, Cilt: 68 Sayı: 2, 1256 - 1264, 01.08.2019

Gülsüm Yeliz Şentürk Salim Yüce

https://doi.org/10.31801/cfsuasmas.516604

Cited By: 7

Öz

In this study, using Darboux frame {T,g,n} of ruled surface ϕ(s,v), the evolute offsets ϕ^{∗}(s,v) with Darboux frame {T^{∗},g^{∗},n^{∗}} of ϕ(s,v) are defined. Characteristic properties of ϕ^{∗}(s,v) as a striction curve, distribution parameter and orthogonal trajectory are investigated using the Darboux frame. The distribution parameters of ruled surfaces ϕ_{T^{∗}}^{∗},ϕ_{g^{∗}}^{∗} and ϕ_{n^{∗}}^{∗} are given. By using Darboux frame of the surfaces we have given the relations between the instantaneous Pfaffian vectors of motions H/H′ and H^{∗}/H^{∗′}, where H={T,g,n} be the moving space along the base curve of ϕ(s,v), H^{∗}={T^{∗},g^{∗},n^{∗}} be the moving space along the base curve of ϕ^{∗}(s,v), H′ and H^{∗′} be fixed Euclidean spaces.

Anahtar Kelimeler

Darboux frame, evolute offset, ruled surface

Kaynakça

Boyer, C.A. History of mathematics, New-York, Wiley, 1968.
Ravani, B. and Ku, T.S. Bertrand offsets of ruled and developable surfaces, Comp Aided Geom Design, 23 (2), (1991), 145--152.
Kasap, E. and Kuruoğlu, N. The Bertrand offsets of ruled surfaces in R₁³, Acta Math. Vietnam, 31 (1), (2006), 39--48.
Kasap, E. and Yüce, S. and Kuruoğlu, N. The Involute-Evolute Offsets of Ruled Surfaces, Iran. J. Sci. Technol. A, (2009), 32 (A2), 195--201.
Orbay, K. and Kasap,E. and Aydemir, İ. Mannheim offsets of ruled surfaces. Math Problems Engineering, (2009), Article Id 160917.
Yoon, D.W. On the evolute offsets of ruled surfaces in Minkowski 3-space, Turkish Journal of Mathematics, 40, (2016), 594--604.
Şentürk, G.Y. and Yüce, S. Characteristic properties of the ruled surface with Darboux Frame in E³, Kuwait J Sci, 42 (2), (2015) 14--33.
Şentürk, G.Y. and Yüce, S. Bertrand offsets of ruled surfaces with Darboux Frame, Results in Mathematics, 72(3), (2017) 1151-1159.
Bektaş, Ö. and Yüce, S. Special involute-evolute partner D-curves in E³, European Journal of Pure and Applied Mathematics, (2013) 6(1), 20--29.
Darboux, G. Leçons sur la Thèorie gènèrale des Sufaces I-II-III-IV, Gauthier- Villars, Paris, 1896.

Yıl 2019, Cilt: 68 Sayı: 2, 1256 - 1264, 01.08.2019

Gülsüm Yeliz Şentürk Salim Yüce

https://doi.org/10.31801/cfsuasmas.516604

Cited By: 7

Öz

Kaynakça

Boyer, C.A. History of mathematics, New-York, Wiley, 1968.
Ravani, B. and Ku, T.S. Bertrand offsets of ruled and developable surfaces, Comp Aided Geom Design, 23 (2), (1991), 145--152.
Kasap, E. and Kuruoğlu, N. The Bertrand offsets of ruled surfaces in R₁³, Acta Math. Vietnam, 31 (1), (2006), 39--48.
Kasap, E. and Yüce, S. and Kuruoğlu, N. The Involute-Evolute Offsets of Ruled Surfaces, Iran. J. Sci. Technol. A, (2009), 32 (A2), 195--201.
Orbay, K. and Kasap,E. and Aydemir, İ. Mannheim offsets of ruled surfaces. Math Problems Engineering, (2009), Article Id 160917.
Yoon, D.W. On the evolute offsets of ruled surfaces in Minkowski 3-space, Turkish Journal of Mathematics, 40, (2016), 594--604.
Şentürk, G.Y. and Yüce, S. Characteristic properties of the ruled surface with Darboux Frame in E³, Kuwait J Sci, 42 (2), (2015) 14--33.
Şentürk, G.Y. and Yüce, S. Bertrand offsets of ruled surfaces with Darboux Frame, Results in Mathematics, 72(3), (2017) 1151-1159.
Bektaş, Ö. and Yüce, S. Special involute-evolute partner D-curves in E³, European Journal of Pure and Applied Mathematics, (2013) 6(1), 20--29.
Darboux, G. Leçons sur la Thèorie gènèrale des Sufaces I-II-III-IV, Gauthier- Villars, Paris, 1896.

Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Makaleler
Yazarlar	Gülsüm Yeliz Şentürk Bu kişi benim 0000-0002-8647-1801 Salim Yüce 0000-0002-8296-6495
Yayımlanma Tarihi	1 Ağustos 2019
Gönderilme Tarihi	19 Ekim 2017
Kabul Tarihi	8 Ocak 2019
Yayımlandığı Sayı	Yıl 2019 Cilt: 68 Sayı: 2

Kaynak Göster

APA	Şentürk, G. Y., & Yüce, S. (2019). On the evolute offsets of ruled surfaces using the Darboux frame. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1256-1264. https://doi.org/10.31801/cfsuasmas.516604
AMA	Şentürk GY, Yüce S. On the evolute offsets of ruled surfaces using the Darboux frame. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2019;68(2):1256-1264. doi:10.31801/cfsuasmas.516604
Chicago	Şentürk, Gülsüm Yeliz, ve Salim Yüce. “On the Evolute Offsets of Ruled Surfaces Using the Darboux Frame”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 2 (Ağustos 2019): 1256-64. https://doi.org/10.31801/cfsuasmas.516604.
EndNote	Şentürk GY, Yüce S (01 Ağustos 2019) On the evolute offsets of ruled surfaces using the Darboux frame. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1256–1264.
IEEE	G. Y. Şentürk ve S. Yüce, “On the evolute offsets of ruled surfaces using the Darboux frame”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 2, ss. 1256–1264, 2019, doi: 10.31801/cfsuasmas.516604.
ISNAD	Şentürk, Gülsüm Yeliz - Yüce, Salim. “On the Evolute Offsets of Ruled Surfaces Using the Darboux Frame”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (Ağustos 2019), 1256-1264. https://doi.org/10.31801/cfsuasmas.516604.
JAMA	Şentürk GY, Yüce S. On the evolute offsets of ruled surfaces using the Darboux frame. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1256–1264.
MLA	Şentürk, Gülsüm Yeliz ve Salim Yüce. “On the Evolute Offsets of Ruled Surfaces Using the Darboux Frame”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 2, 2019, ss. 1256-64, doi:10.31801/cfsuasmas.516604.
Vancouver	Şentürk GY, Yüce S. On the evolute offsets of ruled surfaces using the Darboux frame. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1256-64.