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
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.
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
Şenyurt, S., Canlı, D., & Çan, E. (2022). Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I. Turkish Journal of Science, 7(1), 31-42.
AMA
Şenyurt S, Canlı D, Çan E. Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I. TJOS. Nisan 2022;7(1):31-42.
Chicago
Şenyurt, Süleyman, Davut Canlı, ve Elif Çan. “Some Special Smarandache Ruled Surfaces by Frenet Frame in $E^3$ -I”. Turkish Journal of Science 7, sy. 1 (Nisan 2022): 31-42.
EndNote
Şenyurt S, Canlı D, Çan E (01 Nisan 2022) Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I. Turkish Journal of Science 7 1 31–42.
IEEE
S. Şenyurt, D. Canlı, ve E. Çan, “Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I”, TJOS, c. 7, sy. 1, ss. 31–42, 2022.
ISNAD
Şenyurt, Süleyman vd. “Some Special Smarandache Ruled Surfaces by Frenet Frame in $E^3$ -I”. Turkish Journal of Science 7/1 (Nisan 2022), 31-42.
JAMA
Şenyurt S, Canlı D, Çan E. Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I. TJOS. 2022;7:31–42.
MLA
Şenyurt, Süleyman vd. “Some Special Smarandache Ruled Surfaces by Frenet Frame in $E^3$ -I”. Turkish Journal of Science, c. 7, sy. 1, 2022, ss. 31-42.
Vancouver
Şenyurt S, Canlı D, Çan E. Some special Smarandache ruled surfaces by Frenet Frame in $E^3$ -I. TJOS. 2022;7(1):31-42.