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Smarandache Curves According to q-Frame in Minkowski 3-Space

Year 2019, Volume: 2 Issue: 2, 110 - 118, 25.11.2019

Cumali Ekici , Merve Büşra Göksel Mustafa Dede

Abstract

In this study, we investigate special Smarandache curves according to q-frame in Minkowski 3-space and we give some differential geometric properties of Smarandache curves.

Keywords

Frenet frame Natural curvatures q-frame Smarandache curves

References

  • [1] A. T. Ali, Special Smarandache curves in the Euclidean space, International Journal of Mathematical Combinatorics, 2 (2010), 30-36.
  • [2] K. Akutagawa and S. Nishikawa, The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Tohoku Mathematical Journal, 42 (1990), 67-82.
  • [3] C. Ashbacher, Smarandache geometries, Smarandache Notions Journal, 8(1-3) (1997), 212-215.
  • [4] Ö. Bekta¸s and S. Yüce, Special Smarandache curves according to Darboux frame in E3, Rom. J. Math. Comput. Sci., 3 (2013), 48-59.
  • [5] R. L. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly 82 (1975), 246-251.
  • [6] J. Bloomenthal, Calculation of Reference Frames Along a Space Curve, Graphics gems, Academic Press Professional Inc., San Diego, CA, 1990.
  • [7] W. B. Bonnor, Null curves in a Minkowski space-time, Tensor, 20 (1969), 229-242.
  • [8] P. M. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Englewood Cliffs, New York, 1976.
  • [9] S. Coquillart, Computing offsets of B-spline curves, Computer-Aided Design, 19(6) (1987), 305-09.
  • [10] M. Çetin, Y. Tunçer and M.K. Karacan, Smarandache curves according to Bishop frame in Euclidean 3-space, General Mathematics Notes, 20(2) (2014), 50-66.
  • [11] M. Dede, C. Ekici and A. Görgülü, Directional q-frame along a space curve, IJARCSSE, 5(12) (2015), 775-780.
  • [12] M. Dede, C. Ekici, H. Tozak, Directional tubular surfaces, International Journal of Algebra 9(12) (2015), 527-535.
  • [13] M. Dede, C. Ekici and ˙I. A. Güven, Directional Bertrand curves, GU J Sci, 31(1) (2018), 202-211.
  • [14] M. Dede, G. Tarım and C. Ekici, Timelike directional Bertrand curves in Minkowski space, 15th International Geometry Symposium, Amasya-Turkey, 2017.
  • [15] C. Ekici, M. Dede and H. Tozak, Timelike directional tubular surfaces, Journal of Mathematical Analysis 8(5) (2017), 1-11.
  • [16] C. Ekici, M.B. Göksel and M. Dede, Smarandache curves according to q-frame in Euclidean 3-space, 16th International Geometry Symposium, Manisa-Turkey, 2018.
  • [17] A. Gray, S. Salamon and E. Abbena, Modern differential geometry of curves and surfaces with Mathematica, Chapman and Hall/CRC, 2006.
  • [18] H. Guggenheimer, Computing frames along a trajectory, Comput. Aided Geom. Des., 6 (1989), 77-78.
  • [19] F. Karaman, Özel Smarandache e˘grileri, Anadolu Üniv., Bilecik ¸Seyh Edebali Üniv. Fen Bilimleri Ens. Matematik, 2015.
  • [20] W. Kuhnel, Differential geometry: curves-surfaces-manifolds, Braunscheweig, Weisbaden, 1999.
  • [21] T. Maekawa, N.M. Patrikalakis, T. Sakkalis, G. Yu, Analysis and applications of pipe surfaces, Comput. Aided Geom. Design, 15 (1988), 437-458.
  • [22] B. O’Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, 1983.
  • [23] T. Otsuki, Differential geometry (Japanese), Asakura Shoten, Tokyo, 1961.
  • [24] H. Shin, S. K. Yoo, S. K. Cho, W. H. Chung, Directional offset of a spatial curve for practical engineering design, ICCSA, 3 (2003), 711-720.
  • [25] S. ¸Senyurt, S. Sivas, Smarandache e˘grilerine ait bir uygulama, Ordu Üniv. Bil. Tek. Derg. 3(1) (2013), 46-60.
  • [26] K. Ta¸sköprü and M. Tosun, Smarandache curves on S2, Boletim da Sociedade paranaense de Matemtica 3 srie. 32(1) (2014), 51-59.
  • [27] Y. Tunçer and S. Ünal, New representations of Bertrand pairs in Euclidean 3-space, Applied Mathematics and Computation, 219 (2012), 1833-1842.
  • [28] M. Turgut and S. Yılmaz, Smarandache curves in Minkowski space-time, International Journal of Mathematical Combinatorics, 3 (2008), 51-55.
  • [29] W. Wang, B. Jüttler, D. Zheng and Y. Liu, Computation of rotation minimizing frame, ACM Trans. Graph, 27(1) (2008), 18 pages.
  • [30] S. Yılmaz and M. Turgut, A new version of Bishop frame and an application to spherical images, J. Math. Anal. Appl., 371 (2010), 764-776.

Year 2019, Volume: 2 Issue: 2, 110 - 118, 25.11.2019

Cumali Ekici , Merve Büşra Göksel Mustafa Dede

Abstract

References

  • [1] A. T. Ali, Special Smarandache curves in the Euclidean space, International Journal of Mathematical Combinatorics, 2 (2010), 30-36.
  • [2] K. Akutagawa and S. Nishikawa, The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Tohoku Mathematical Journal, 42 (1990), 67-82.
  • [3] C. Ashbacher, Smarandache geometries, Smarandache Notions Journal, 8(1-3) (1997), 212-215.
  • [4] Ö. Bekta¸s and S. Yüce, Special Smarandache curves according to Darboux frame in E3, Rom. J. Math. Comput. Sci., 3 (2013), 48-59.
  • [5] R. L. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly 82 (1975), 246-251.
  • [6] J. Bloomenthal, Calculation of Reference Frames Along a Space Curve, Graphics gems, Academic Press Professional Inc., San Diego, CA, 1990.
  • [7] W. B. Bonnor, Null curves in a Minkowski space-time, Tensor, 20 (1969), 229-242.
  • [8] P. M. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Englewood Cliffs, New York, 1976.
  • [9] S. Coquillart, Computing offsets of B-spline curves, Computer-Aided Design, 19(6) (1987), 305-09.
  • [10] M. Çetin, Y. Tunçer and M.K. Karacan, Smarandache curves according to Bishop frame in Euclidean 3-space, General Mathematics Notes, 20(2) (2014), 50-66.
  • [11] M. Dede, C. Ekici and A. Görgülü, Directional q-frame along a space curve, IJARCSSE, 5(12) (2015), 775-780.
  • [12] M. Dede, C. Ekici, H. Tozak, Directional tubular surfaces, International Journal of Algebra 9(12) (2015), 527-535.
  • [13] M. Dede, C. Ekici and ˙I. A. Güven, Directional Bertrand curves, GU J Sci, 31(1) (2018), 202-211.
  • [14] M. Dede, G. Tarım and C. Ekici, Timelike directional Bertrand curves in Minkowski space, 15th International Geometry Symposium, Amasya-Turkey, 2017.
  • [15] C. Ekici, M. Dede and H. Tozak, Timelike directional tubular surfaces, Journal of Mathematical Analysis 8(5) (2017), 1-11.
  • [16] C. Ekici, M.B. Göksel and M. Dede, Smarandache curves according to q-frame in Euclidean 3-space, 16th International Geometry Symposium, Manisa-Turkey, 2018.
  • [17] A. Gray, S. Salamon and E. Abbena, Modern differential geometry of curves and surfaces with Mathematica, Chapman and Hall/CRC, 2006.
  • [18] H. Guggenheimer, Computing frames along a trajectory, Comput. Aided Geom. Des., 6 (1989), 77-78.
  • [19] F. Karaman, Özel Smarandache e˘grileri, Anadolu Üniv., Bilecik ¸Seyh Edebali Üniv. Fen Bilimleri Ens. Matematik, 2015.
  • [20] W. Kuhnel, Differential geometry: curves-surfaces-manifolds, Braunscheweig, Weisbaden, 1999.
  • [21] T. Maekawa, N.M. Patrikalakis, T. Sakkalis, G. Yu, Analysis and applications of pipe surfaces, Comput. Aided Geom. Design, 15 (1988), 437-458.
  • [22] B. O’Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, 1983.
  • [23] T. Otsuki, Differential geometry (Japanese), Asakura Shoten, Tokyo, 1961.
  • [24] H. Shin, S. K. Yoo, S. K. Cho, W. H. Chung, Directional offset of a spatial curve for practical engineering design, ICCSA, 3 (2003), 711-720.
  • [25] S. ¸Senyurt, S. Sivas, Smarandache e˘grilerine ait bir uygulama, Ordu Üniv. Bil. Tek. Derg. 3(1) (2013), 46-60.
  • [26] K. Ta¸sköprü and M. Tosun, Smarandache curves on S2, Boletim da Sociedade paranaense de Matemtica 3 srie. 32(1) (2014), 51-59.
  • [27] Y. Tunçer and S. Ünal, New representations of Bertrand pairs in Euclidean 3-space, Applied Mathematics and Computation, 219 (2012), 1833-1842.
  • [28] M. Turgut and S. Yılmaz, Smarandache curves in Minkowski space-time, International Journal of Mathematical Combinatorics, 3 (2008), 51-55.
  • [29] W. Wang, B. Jüttler, D. Zheng and Y. Liu, Computation of rotation minimizing frame, ACM Trans. Graph, 27(1) (2008), 18 pages.
  • [30] S. Yılmaz and M. Turgut, A new version of Bishop frame and an application to spherical images, J. Math. Anal. Appl., 371 (2010), 764-776.
There are 30 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Cumali Ekici

Merve Büşra Göksel This is me 0000-0001-8207-8212

Mustafa Dede 0000-0003-2652-637X

Publication Date November 25, 2019
Acceptance Date September 27, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Ekici, C., Göksel, M. B., & Dede, M. (2019). Smarandache Curves According to q-Frame in Minkowski 3-Space. Conference Proceedings of Science and Technology, 2(2), 110-118.
AMA Ekici C, Göksel MB, Dede M. Smarandache Curves According to q-Frame in Minkowski 3-Space. Conference Proceedings of Science and Technology. November 2019;2(2):110-118.
Chicago Ekici, Cumali, Merve Büşra Göksel, and Mustafa Dede. “Smarandache Curves According to Q-Frame in Minkowski 3-Space”. Conference Proceedings of Science and Technology 2, no. 2 (November 2019): 110-18.
EndNote Ekici C, Göksel MB, Dede M (November 1, 2019) Smarandache Curves According to q-Frame in Minkowski 3-Space. Conference Proceedings of Science and Technology 2 2 110–118.
IEEE C. Ekici, M. B. Göksel, and M. Dede, “Smarandache Curves According to q-Frame in Minkowski 3-Space”, Conference Proceedings of Science and Technology, vol. 2, no. 2, pp. 110–118, 2019.
ISNAD Ekici, Cumali et al. “Smarandache Curves According to Q-Frame in Minkowski 3-Space”. Conference Proceedings of Science and Technology 2/2 (November 2019), 110-118.
JAMA Ekici C, Göksel MB, Dede M. Smarandache Curves According to q-Frame in Minkowski 3-Space. Conference Proceedings of Science and Technology. 2019;2:110–118.
MLA Ekici, Cumali et al. “Smarandache Curves According to Q-Frame in Minkowski 3-Space”. Conference Proceedings of Science and Technology, vol. 2, no. 2, 2019, pp. 110-8.
Vancouver Ekici C, Göksel MB, Dede M. Smarandache Curves According to q-Frame in Minkowski 3-Space. Conference Proceedings of Science and Technology. 2019;2(2):110-8.
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