Research Article
Year 2016,
Volume: 29 Issue: 1, 69 - 77, 21.03.2016
Abstract
In this study, we give special Smarandache curves according to the Sabban frame in hyperbolic space and new Smarandache partners in de Sitter space. The existence of duality between Smarandache curves in hyperbolic and de Sitter spaces is obtained. We also describe how we can draw pictures of Smarandache partners in de Sitter space of a curve in hyperbolic space. Finally, two examples are given to illustrate our main results.
References
- M.Turgut and S.Yilmaz, "Smarandache Curves in Minkowski Space-time", International J. Math. Combin., Vol.3 (2008), 51-55.
- K. Taskopru and M. Tosun, "Smarandache Curves on S2", Bol. Soc. Paran. Mat. (3s.)Vol. 32(1) (2014), 51-59.
- B. O'neill, Semi-Riemannian Geometry with Applications to Relativity. Academic Press, San Diego, 1983.
- C. Ashbacher, Smarandache geometries, Smarandache Notions Journal, Vol. 8, no. 13 (1997) pp. 212215.
- E. B. Koc Ozturk, U. Ozturk, K. Ilarslan and E. Nesovic, "On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space", Int. J. of Math. and Math. Sci., 7 pp., (2013), Art. ID 658670.
- T. Sato, "Pseudo-spherical evolutes of curves on a space like surface in three dimensional Lorentz-Minkowski space", J. Geom. Vol.103(2) (2012), 319-331.
- S. Izumiya, D. H. Pei, T. Sano and E. Torii, "Evolutes of hyperbolic plane curves", Acta Math. Sinica (English Series), Vol.20(3) (2004), 543-550.
- V. Asil, T. Korpinar and S. Bas, "Inextensible ows of timelike curves with Sabban frame in S2 1 ", Siauliai Math. Semin. Vol.7(15) (2012), 5-12.
- M. Cetin, Y. Tuncer and M. K. Karacan, "Smarandache Curves According to Bishop Frame in Euclidean 3- Space", Gen. Math. Notes, Vol. 20(2) (2014), 50-66.
- A.Yakut, M.Savas and T.Tamirci, "The Smarandache Curves on S^2_1 and Its Duality on H^2_0 ", Journal of Applied Mathematics, In press (2014).
- A.T. Ali, "Special Smarandache Curves in the Euclidean Space", International Journal of Mathematical Combina-torics Vol.2 (2010) 30-36.
- T. Tamirci, "Curves on surface in three dimensional Lorentz Minkowski space", Master Thesis, Nigde, 2014.
Year 2016,
Volume: 29 Issue: 1, 69 - 77, 21.03.2016
Abstract
References
- M.Turgut and S.Yilmaz, "Smarandache Curves in Minkowski Space-time", International J. Math. Combin., Vol.3 (2008), 51-55.
- K. Taskopru and M. Tosun, "Smarandache Curves on S2", Bol. Soc. Paran. Mat. (3s.)Vol. 32(1) (2014), 51-59.
- B. O'neill, Semi-Riemannian Geometry with Applications to Relativity. Academic Press, San Diego, 1983.
- C. Ashbacher, Smarandache geometries, Smarandache Notions Journal, Vol. 8, no. 13 (1997) pp. 212215.
- E. B. Koc Ozturk, U. Ozturk, K. Ilarslan and E. Nesovic, "On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space", Int. J. of Math. and Math. Sci., 7 pp., (2013), Art. ID 658670.
- T. Sato, "Pseudo-spherical evolutes of curves on a space like surface in three dimensional Lorentz-Minkowski space", J. Geom. Vol.103(2) (2012), 319-331.
- S. Izumiya, D. H. Pei, T. Sano and E. Torii, "Evolutes of hyperbolic plane curves", Acta Math. Sinica (English Series), Vol.20(3) (2004), 543-550.
- V. Asil, T. Korpinar and S. Bas, "Inextensible ows of timelike curves with Sabban frame in S2 1 ", Siauliai Math. Semin. Vol.7(15) (2012), 5-12.
- M. Cetin, Y. Tuncer and M. K. Karacan, "Smarandache Curves According to Bishop Frame in Euclidean 3- Space", Gen. Math. Notes, Vol. 20(2) (2014), 50-66.
- A.Yakut, M.Savas and T.Tamirci, "The Smarandache Curves on S^2_1 and Its Duality on H^2_0 ", Journal of Applied Mathematics, In press (2014).
- A.T. Ali, "Special Smarandache Curves in the Euclidean Space", International Journal of Mathematical Combina-torics Vol.2 (2010) 30-36.
- T. Tamirci, "Curves on surface in three dimensional Lorentz Minkowski space", Master Thesis, Nigde, 2014.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | March 21, 2016 |
| Published in Issue | Year 2016 Volume: 29 Issue: 1 |