Another application of Smarandache based  ruled surfaces  with  the Darboux  vector according to Frenet frame in $E^{3}$

Süleyman Şenyurt; Davut Canlı; Elif Çan; Sümeyye Gür Mazlum

Makale detayları

Another application of Smarandache based ruled surfaces with the Darboux vector according to Frenet frame in $E^{3}$

Yazarlar:

Süleyman Şenyurt | Davut Canlı | Elif Çan | Sümeyye Gür Mazlum

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 4, pp.880-906

Belge Tipi:

Makale

Yayın Tarihi:

12/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001303607

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 In this study, we first define the Smarandache curves derived from the Frenet vectors and the Darboux vector of any curve. Then, we construct new ruled surfaces along these Smarandache curves with the direction vectors obtained from the Frenet vectors and the Darboux vector, and give the equations of these surfaces. In addition, we calculate the Gaussian and mean curvatures of these surfaces separately and present the conditions to be minimal and developable for these surfaces. Finally, as an example, we obtain ruled surfaces whose base curves are Vivianis curves and plot the graphics of these surfaces.

 In this study, we first define the Smarandache curves derived from the Frenet vectors and the Darboux vector of any curve. Then, we construct new ruled surfaces along these Smarandache curves with the direction vectors obtained from the Frenet vectors and the Darboux vector, and give the equations of these surfaces. In addition, we calculate the Gaussian and mean curvatures of these surfaces separately and present the conditions to be minimal and developable for these surfaces. Finally, as an example, we obtain ruled surfaces whose base curves are Vivianis curves and plot the graphics of these surfaces.

 In this study, we first define the Smarandache curves derived from the Frenet vectors and the Darboux vector of any curve. Then, we construct new ruled surfaces along these Smarandache curves with the direction vectors obtained from the Frenet vectors and the Darboux vector, and give the equations of these surfaces. In addition, we calculate the Gaussian and mean curvatures of these surfaces separately and present the conditions to be minimal and developable for these surfaces. Finally, as an example, we obtain ruled surfaces whose base curves are Vivianis curves and plot the graphics of these surfaces.

 In this study, we first define the Smarandache curves derived from the Frenet vectors and the Darboux vector of any curve. Then, we construct new ruled surfaces along these Smarandache curves with the direction vectors obtained from the Frenet vectors and the Darboux vector, and give the equations of these surfaces. In addition, we calculate the Gaussian and mean curvatures of these surfaces separately and present the conditions to be minimal and developable for these surfaces. Finally, as an example, we obtain ruled surfaces whose base curves are Vivianis curves and plot the graphics of these surfaces.

Makale detayları

Another application of Smarandache based ruled surfaces with the Darboux vector according to Frenet frame in $E^{3}$

Yazarlar:

Süleyman Şenyurt | Davut Canlı | Elif Çan | Sümeyye Gür Mazlum

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 4, pp.880-906

Belge Tipi:

Makale

Yayın Tarihi:

12/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001303607

pISSN:

1303-5991

Smarandache curve

ruled surfaces

mean curvature

Gaussian curvature

Viviani's curve

Sayı

Makale detayları

Another application of Smarandache based ruled surfaces with the Darboux vector according to Frenet frame in $E^{3}$

Yazarlar: Süleyman Şenyurt | Davut Canlı | Elif Çan | Sümeyye Gür Mazlum

Yayıncı: Ankara University

Ana Başlıklar: Mathematical Sciences

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 4, pp.880-906

Belge Tipi: Makale

Yayın Tarihi: 12/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001303607

pISSN: 1303-5991

Smarandache curve

ruled surfaces

mean curvature

Gaussian curvature

Viviani's curve

Sayı

Yazarlar:

Süleyman Şenyurt | Davut Canlı | Elif Çan | Sümeyye Gür Mazlum

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 4, pp.880-906

Belge Tipi:

Makale

Yayın Tarihi:

12/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001303607

pISSN:

1303-5991