Yıl 2022,
Cilt: 7 Sayı: 1, 31 - 42, 30.04.2022
Süleyman Şenyurt
,
Davut Canlı
,
Elif Çan
Kaynakça
- Pottmann, H., Asperl, A., Hofer, M. ve Killian, A., Architectural Geometry, Bentley, D. (ed.), First Edition, Bentley Institute Press, 2007
- Berk, A., A Structural Basis for Surface Discretization of Free Form Structures: Integration of Geometry, Materials and Fabrication, Ph. D Thesis, Michigan University, ABD, 2012
- Do-Carmo, P.M., Differential geometry of curvesand surfaces. IMPA, 1976
- Fenchel,W., On the Differential Geometry of Closed Space Curves, Bulletin of American Mathematical Society, 57(44-54), 1951
- Gray A. Modern differential geometry of curves and surfaces with Mathematica, 1997
- Pressley A.,Elementary Differential Geometry, Second Edition, Springer London, 2010
- Struik D. J., Lectures on classical differential geometry, Addison-Wesley Publishing Company, 1961
- Ouarab, S., Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E3, Hindawi Abstract and Applied Analysis, Vol. 2021, Article ID 5526536, 8 pages
- Ouarab, S., Smarandache ruled Surfaces according to Darboux Frame in $E^3$, Hindawi Journal of Mathematics, Vol. 2021, Article ID 9912624, 10 pages
- Ouarab,S., NC-Smarandache ruled surface and NW-Smarandache ruled surface according to alternative moving frame in $E^3$, Hindawi Journal of Mathematics ,Vol. 2021, Article ID 9951434, 6 pages
- Turgut, N., S. Yılmaz, S., “Smarandache curves in Minkowski space-time,” International Journal of Mathematical Combinatorics, vol. 3, pp. 51–55, 2008.
- Ali, A.T., Special Smarandache curves in the Euclidean space, International Journal of Mathematical Combinatorics, 2(2010),30-36, 2010.
- Şenyurt, S., Sivas, S., An Application of Smarandache Curve, Ordu Univ. J. Sci. Tech., 3(1),46-6, 2013
Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I
Yıl 2022,
Cilt: 7 Sayı: 1, 31 - 42, 30.04.2022
Süleyman Şenyurt
,
Davut Canlı
,
Elif Çan
Öz
The paper introduces some new special ruled surfaces possessing the base as the TNB- Smarandache curve of Frenet frame. The geometric properties such as minimality or developability of each generated surface are examined by Gauss and mean curvatures. An example is also given by considering the famous Viviani’s curve.
Teşekkür
Thanks in advance for your time and consideration on our manuscript.
Kaynakça
- Pottmann, H., Asperl, A., Hofer, M. ve Killian, A., Architectural Geometry, Bentley, D. (ed.), First Edition, Bentley Institute Press, 2007
- Berk, A., A Structural Basis for Surface Discretization of Free Form Structures: Integration of Geometry, Materials and Fabrication, Ph. D Thesis, Michigan University, ABD, 2012
- Do-Carmo, P.M., Differential geometry of curvesand surfaces. IMPA, 1976
- Fenchel,W., On the Differential Geometry of Closed Space Curves, Bulletin of American Mathematical Society, 57(44-54), 1951
- Gray A. Modern differential geometry of curves and surfaces with Mathematica, 1997
- Pressley A.,Elementary Differential Geometry, Second Edition, Springer London, 2010
- Struik D. J., Lectures on classical differential geometry, Addison-Wesley Publishing Company, 1961
- Ouarab, S., Smarandache Ruled Surfaces according to Frenet-Serret Frame of a Regular Curve in E3, Hindawi Abstract and Applied Analysis, Vol. 2021, Article ID 5526536, 8 pages
- Ouarab, S., Smarandache ruled Surfaces according to Darboux Frame in $E^3$, Hindawi Journal of Mathematics, Vol. 2021, Article ID 9912624, 10 pages
- Ouarab,S., NC-Smarandache ruled surface and NW-Smarandache ruled surface according to alternative moving frame in $E^3$, Hindawi Journal of Mathematics ,Vol. 2021, Article ID 9951434, 6 pages
- Turgut, N., S. Yılmaz, S., “Smarandache curves in Minkowski space-time,” International Journal of Mathematical Combinatorics, vol. 3, pp. 51–55, 2008.
- Ali, A.T., Special Smarandache curves in the Euclidean space, International Journal of Mathematical Combinatorics, 2(2010),30-36, 2010.
- Şenyurt, S., Sivas, S., An Application of Smarandache Curve, Ordu Univ. J. Sci. Tech., 3(1),46-6, 2013