On Smarandache Curves in Affine 3-Space

Ufuk Öztürk; Burcu Sarıkaya; Pınar Haskul; Ayşegül Emir

doi:10.53570/jnt.1073323

Research Article

Year 2022, Issue: 38, 61 - 69, 31.03.2022

Ufuk Öztürk , Burcu Sarıkaya , Pınar Haskul , Ayşegül Emir

https://doi.org/10.53570/jnt.1073323

Abstract

References

H. Abdel-Aziz, M. K. Saad, Computation of Smarandache Curves According to Darboux Frame in Minkowski 3-Space, Journal of the Egyptian Mathematical Society 25(4) (2017) 382–390.
A. T. Ali, Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics 2 (2010) 30–36.
O. Bektaş, S. Yüce, Special Smarandache Curves According to Darboux Frame in $E^3$, Romanian Journal of Mathematics and Computer Science 3(1) (2013) 48–59.
M. Çetin, Y. Tuncer, M. K. Karacan, Smarandache Curves According to Bishop Frame in Euclidean 3-Space, General Mathematics Notes 20(2) (2014) 50–66.
M. Elzawy, S. Mosa, Smarandache Curves in the Galilean 4-Space G4, Journal of the Egyptian Mathematical Society 25(1) (2017) 53–56.
T. Kahraman, H. H. Uğurlu, Dual Smarandache Curves and Smarandache Ruled Surfaces, Mathematical Sciences and Applications E-Notes 2(1) (2014) 83–98.
E. B. Koc Ozturk, U. Ozturk, K. İlarslan, E. Nešović, On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space, International Journal of Mathematics and Mathematical Sciences Article ID 658670 (2013) 7 pages.
E. B. Koc Ozturk, U. Ozturk, K. İlarslan, E. Nešović, On Pseudospherical Smarandache Curves in Minkowski 3-Space, Journal of Applied Mathematics Article ID 404521 (2014) 14 pages.
M. Mak, H. Altınbas, Spacelike Smarandache Curves of Timelike Curves in Anti de Sitter 3-Space, International Journal of Mathematical Combinatorics 3 (2016) 1–16.
U. Ozturk, E. B. Koc Ozturk, Smarandache Curves according to Curves on a Spacelike Surface in Minkowski 3-Space, Journal of Discrete Mathematics Article ID 829581 (2014) 10 pages.
U. Ozturk, E. B. Koc Ozturk, K. İlarslan, E. Nešović, On Smarandache Curves Lying in Lightcone in Minkowski 3-Space, Journal of Dynamical Systems and Geometric Theories 12(1) (2014) 81–91.
E. Solouma, Special Equiform Smarandache Curves in Minkowski Space-Time, Journal of the Egyptian Mathematical Society 25(3) (2017) 319–325.
S. Şenyurt, Y. Altun, C. Cevahir, Smarandache Curves According to Sabban Frame Belonging to Mannheim Curves Pair, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68(1) (2019) 500–513.
S. Şenyurt, C. Cevahir, Y. Altun, On the Smarandache Curves of Spatial Quaternionic Involute Curve, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 90(5) (2020) 827–837.
S. Şenyurt, A. Çaliskan, U. Çelik, Smarandache Curves of Bertrand Curves Pair According to Frenet Frame, Boletim da Sociedade Paranaense de Matemàtica 39(5) (2021) 163–173.
K. Taşköprü, M. Tosun, Smarandache Curves on $S^2$, Boletim da Sociedade Paranaense de Matem´atica 32(1) (2014) 51–59.
M. Turgut, S. Yilmaz, Smarandache Curves in Minkowski Space-Time 3 (2008) 51–55.
K. Nomizu, N. Katsumi, T. Sasaki, Affine Differential Geometry: Geometry of Affine Immersions, Cambridge University Press, 1994.
U. Simon, Affine Differential Geometry, in: Handbook of Differential Geometry, Vol. 1, Elsevier, 2000, pp. 905–961.
S. Buchin, Affine Differential Geometry, Gordon and Breach (China), 1983.
N. Hu, Affine Geometry of Space Curves and Homogeneous Surfaces, PhD Dissertation, Department of Mathematics Graduate School of Science Hokkaaido University (2012) Japan.
L. A. Santalò, A Geometrical Characterization for the Affine Differential Invariants of a Space Curve, Bulletin of the American Mathematical Society 52(8) (1946) 625–632.
P. J. Olver, Moving Frames and Differential Invariants in Centro-Affine Geometry, Lobachevskii Journal of Mathematics 31(2) (2010) 77–89.
Y. Tunçer, H. Kocayigit, M. K. Karacan, Indicatrices of Curves in Affine 3-Space, Palestine Journal of Mathematics 9(2) (2020) 858–865.
Y. Tunçer, H. Kocayigit, M. K. Karacan, Naturel Mates of Equiaffine Space Curves in Affine 3-Space, Thermal Science 23(6) (2019) 2149–2157.
Y. Tunçer, Position Vectors of the Curves in Affine 3-Space According to Special Affine Frames, International Journal of Mathematical Combinatorics 2 (2019) 43–59.

On Smarandache Curves in Affine 3-Space

Year 2022, Issue: 38, 61 - 69, 31.03.2022

Ufuk Öztürk , Burcu Sarıkaya , Pınar Haskul , Ayşegül Emir

https://doi.org/10.53570/jnt.1073323

Abstract

In this paper, we introduce Smarandache curves of an affine $C^∞$-curve in affine 3-space. Besides, we present the relationship between the Frenet frames of the curve couple and the Frenet apparatus of each obtained curve.

Keywords

Affine curve, Affine frame, Smarandache curves, Affine $3-$space

References

H. Abdel-Aziz, M. K. Saad, Computation of Smarandache Curves According to Darboux Frame in Minkowski 3-Space, Journal of the Egyptian Mathematical Society 25(4) (2017) 382–390.
A. T. Ali, Special Smarandache Curves in the Euclidean Space, International Journal of Mathematical Combinatorics 2 (2010) 30–36.
O. Bektaş, S. Yüce, Special Smarandache Curves According to Darboux Frame in $E^3$, Romanian Journal of Mathematics and Computer Science 3(1) (2013) 48–59.
M. Çetin, Y. Tuncer, M. K. Karacan, Smarandache Curves According to Bishop Frame in Euclidean 3-Space, General Mathematics Notes 20(2) (2014) 50–66.
M. Elzawy, S. Mosa, Smarandache Curves in the Galilean 4-Space G4, Journal of the Egyptian Mathematical Society 25(1) (2017) 53–56.
T. Kahraman, H. H. Uğurlu, Dual Smarandache Curves and Smarandache Ruled Surfaces, Mathematical Sciences and Applications E-Notes 2(1) (2014) 83–98.
E. B. Koc Ozturk, U. Ozturk, K. İlarslan, E. Nešović, On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space, International Journal of Mathematics and Mathematical Sciences Article ID 658670 (2013) 7 pages.
E. B. Koc Ozturk, U. Ozturk, K. İlarslan, E. Nešović, On Pseudospherical Smarandache Curves in Minkowski 3-Space, Journal of Applied Mathematics Article ID 404521 (2014) 14 pages.
M. Mak, H. Altınbas, Spacelike Smarandache Curves of Timelike Curves in Anti de Sitter 3-Space, International Journal of Mathematical Combinatorics 3 (2016) 1–16.
U. Ozturk, E. B. Koc Ozturk, Smarandache Curves according to Curves on a Spacelike Surface in Minkowski 3-Space, Journal of Discrete Mathematics Article ID 829581 (2014) 10 pages.
U. Ozturk, E. B. Koc Ozturk, K. İlarslan, E. Nešović, On Smarandache Curves Lying in Lightcone in Minkowski 3-Space, Journal of Dynamical Systems and Geometric Theories 12(1) (2014) 81–91.
E. Solouma, Special Equiform Smarandache Curves in Minkowski Space-Time, Journal of the Egyptian Mathematical Society 25(3) (2017) 319–325.
S. Şenyurt, Y. Altun, C. Cevahir, Smarandache Curves According to Sabban Frame Belonging to Mannheim Curves Pair, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68(1) (2019) 500–513.
S. Şenyurt, C. Cevahir, Y. Altun, On the Smarandache Curves of Spatial Quaternionic Involute Curve, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 90(5) (2020) 827–837.
S. Şenyurt, A. Çaliskan, U. Çelik, Smarandache Curves of Bertrand Curves Pair According to Frenet Frame, Boletim da Sociedade Paranaense de Matemàtica 39(5) (2021) 163–173.
K. Taşköprü, M. Tosun, Smarandache Curves on $S^2$, Boletim da Sociedade Paranaense de Matem´atica 32(1) (2014) 51–59.
M. Turgut, S. Yilmaz, Smarandache Curves in Minkowski Space-Time 3 (2008) 51–55.
K. Nomizu, N. Katsumi, T. Sasaki, Affine Differential Geometry: Geometry of Affine Immersions, Cambridge University Press, 1994.
U. Simon, Affine Differential Geometry, in: Handbook of Differential Geometry, Vol. 1, Elsevier, 2000, pp. 905–961.
S. Buchin, Affine Differential Geometry, Gordon and Breach (China), 1983.
N. Hu, Affine Geometry of Space Curves and Homogeneous Surfaces, PhD Dissertation, Department of Mathematics Graduate School of Science Hokkaaido University (2012) Japan.
L. A. Santalò, A Geometrical Characterization for the Affine Differential Invariants of a Space Curve, Bulletin of the American Mathematical Society 52(8) (1946) 625–632.
P. J. Olver, Moving Frames and Differential Invariants in Centro-Affine Geometry, Lobachevskii Journal of Mathematics 31(2) (2010) 77–89.
Y. Tunçer, H. Kocayigit, M. K. Karacan, Indicatrices of Curves in Affine 3-Space, Palestine Journal of Mathematics 9(2) (2020) 858–865.
Y. Tunçer, H. Kocayigit, M. K. Karacan, Naturel Mates of Equiaffine Space Curves in Affine 3-Space, Thermal Science 23(6) (2019) 2149–2157.
Y. Tunçer, Position Vectors of the Curves in Affine 3-Space According to Special Affine Frames, International Journal of Mathematical Combinatorics 2 (2019) 43–59.

There are 26 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Article
Authors	Ufuk Öztürk 0000-0002-8800-7869 Burcu Sarıkaya 0000-0002-5866-3144 Pınar Haskul 0000-0002-2191-8449 Ayşegül Emir 0000-0002-7295-4925
Publication Date	March 31, 2022
Submission Date	February 14, 2022
Published in Issue	Year 2022 Issue: 38

Cite

APA	Öztürk, U., Sarıkaya, B., Haskul, P., Emir, A. (2022). On Smarandache Curves in Affine 3-Space. Journal of New Theory(38), 61-69. https://doi.org/10.53570/jnt.1073323
AMA	Öztürk U, Sarıkaya B, Haskul P, Emir A. On Smarandache Curves in Affine 3-Space. JNT. March 2022;(38):61-69. doi:10.53570/jnt.1073323
Chicago	Öztürk, Ufuk, Burcu Sarıkaya, Pınar Haskul, and Ayşegül Emir. “On Smarandache Curves in Affine 3-Space”. Journal of New Theory, no. 38 (March 2022): 61-69. https://doi.org/10.53570/jnt.1073323.
EndNote	Öztürk U, Sarıkaya B, Haskul P, Emir A (March 1, 2022) On Smarandache Curves in Affine 3-Space. Journal of New Theory 38 61–69.
IEEE	U. Öztürk, B. Sarıkaya, P. Haskul, and A. Emir, “On Smarandache Curves in Affine 3-Space”, JNT, no. 38, pp. 61–69, March 2022, doi: 10.53570/jnt.1073323.
ISNAD	Öztürk, Ufuk et al. “On Smarandache Curves in Affine 3-Space”. Journal of New Theory 38 (March 2022), 61-69. https://doi.org/10.53570/jnt.1073323.
JAMA	Öztürk U, Sarıkaya B, Haskul P, Emir A. On Smarandache Curves in Affine 3-Space. JNT. 2022;:61–69.
MLA	Öztürk, Ufuk et al. “On Smarandache Curves in Affine 3-Space”. Journal of New Theory, no. 38, 2022, pp. 61-69, doi:10.53570/jnt.1073323.
Vancouver	Öztürk U, Sarıkaya B, Haskul P, Emir A. On Smarandache Curves in Affine 3-Space. JNT. 2022(38):61-9.

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